LMFDB - Embedded newform 152.2.t.a.101.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(5,152)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("152.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.18
Character	$\chi$	$=$	152.101
Dual form			152.2.t.a.149.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40405 + 0.169229i) q^{2} +(0.945944 - 2.59896i) q^{3} +(1.94272 + 0.475212i) q^{4} +(-1.15070 + 0.202899i) q^{5} +(1.76797 - 3.48899i) q^{6} +(-2.48117 + 4.29751i) q^{7} +(2.64726 + 0.995986i) q^{8} +(-3.56165 - 2.98858i) q^{9} +O(q^{10})$	\(q+(1.40405 + 0.169229i) q^{2} +(0.945944 - 2.59896i) q^{3} +(1.94272 + 0.475212i) q^{4} +(-1.15070 + 0.202899i) q^{5} +(1.76797 - 3.48899i) q^{6} +(-2.48117 + 4.29751i) q^{7} +(2.64726 + 0.995986i) q^{8} +(-3.56165 - 2.98858i) q^{9} +(-1.64997 + 0.0901496i) q^{10} +(-1.12791 + 0.651199i) q^{11} +(3.07276 - 4.59954i) q^{12} +(-1.56654 - 4.30402i) q^{13} +(-4.21095 + 5.61404i) q^{14} +(-0.561168 + 3.18254i) q^{15} +(3.54835 + 1.84641i) q^{16} +(2.55523 - 2.14409i) q^{17} +(-4.49499 - 4.79886i) q^{18} +(-0.369712 + 4.34319i) q^{19} +(-2.33190 - 0.152648i) q^{20} +(8.82201 + 10.5137i) q^{21} +(-1.69384 + 0.723442i) q^{22} +(-0.0598623 + 0.339496i) q^{23} +(5.09269 - 5.93799i) q^{24} +(-3.41553 + 1.24315i) q^{25} +(-1.47113 - 6.30818i) q^{26} +(-3.95069 + 2.28093i) q^{27} +(-6.86245 + 7.16979i) q^{28} +(0.903650 - 1.07693i) q^{29} +(-1.32649 + 4.37349i) q^{30} +(2.59290 - 4.49103i) q^{31} +(4.66960 + 3.19294i) q^{32} +(0.625501 + 3.54739i) q^{33} +(3.95051 - 2.57800i) q^{34} +(1.98311 - 5.44855i) q^{35} +(-5.49910 - 7.49853i) q^{36} -3.14124i q^{37} +(-1.25409 + 6.03550i) q^{38} -12.6678 q^{39} +(-3.24828 - 0.608951i) q^{40} +(8.84858 + 3.22062i) q^{41} +(10.6073 + 16.2547i) q^{42} +(-6.63623 + 1.17015i) q^{43} +(-2.50067 + 0.729103i) q^{44} +(4.70476 + 2.71629i) q^{45} +(-0.141502 + 0.466539i) q^{46} +(-0.689587 - 0.578632i) q^{47} +(8.15528 - 7.47542i) q^{48} +(-8.81238 - 15.2635i) q^{49} +(-5.00596 + 1.16744i) q^{50} +(-3.15530 - 8.66913i) q^{51} +(-0.998025 - 9.10596i) q^{52} +(-1.26559 - 0.223157i) q^{53} +(-5.93297 + 2.53397i) q^{54} +(1.16575 - 0.978183i) q^{55} +(-10.8486 + 8.90543i) q^{56} +(10.9381 + 5.06928i) q^{57} +(1.45102 - 1.35914i) q^{58} +(-6.06841 - 7.23205i) q^{59} +(-2.60258 + 5.91613i) q^{60} +(-2.91105 - 0.513296i) q^{61} +(4.40057 - 5.86684i) q^{62} +(21.6805 - 7.89106i) q^{63} +(6.01602 + 5.27328i) q^{64} +(2.67589 + 4.63477i) q^{65} +(0.277915 + 5.08657i) q^{66} +(-1.95759 + 2.33296i) q^{67} +(5.98300 - 2.95110i) q^{68} +(0.825710 + 0.476724i) q^{69} +(3.70644 - 7.31445i) q^{70} +(1.96983 + 11.1714i) q^{71} +(-6.45205 - 11.4589i) q^{72} +(-1.39362 - 0.507236i) q^{73} +(0.531588 - 4.41046i) q^{74} +10.0528i q^{75} +(-2.78218 + 8.26193i) q^{76} -6.46293i q^{77} +(-17.7863 - 2.14376i) q^{78} +(8.75250 + 3.18565i) q^{79} +(-4.45770 - 1.40470i) q^{80} +(-0.231166 - 1.31101i) q^{81} +(11.8788 + 6.01935i) q^{82} +(11.1997 + 6.46616i) q^{83} +(12.1425 + 24.6175i) q^{84} +(-2.50526 + 2.98565i) q^{85} +(-9.51564 + 0.519906i) q^{86} +(-1.94409 - 3.36726i) q^{87} +(-3.63446 + 0.600514i) q^{88} +(2.44335 - 0.889305i) q^{89} +(6.14605 + 4.61000i) q^{90} +(22.3834 + 3.94680i) q^{91} +(-0.277628 + 0.631099i) q^{92} +(-9.21927 - 10.9871i) q^{93} +(-0.870295 - 0.929128i) q^{94} +(-0.455802 - 5.07271i) q^{95} +(12.7155 - 9.11576i) q^{96} +(-2.82277 + 2.36859i) q^{97} +(-9.79002 - 22.9220i) q^{98} +(5.96338 + 1.05151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.40405	+	0.169229i	0.992815	+	0.119663i
$2$	1.40405	+	0.169229i	0.992815	+	0.119663i
$3$	0.945944	−	2.59896i	0.546141	−	1.50051i	−0.292738	−	0.956193i	$-0.594566\pi$
$3$	0.945944	−	2.59896i	0.546141	−	1.50051i	0.838879	−	0.544318i	$-0.183211\pi$
$4$	1.94272	+	0.475212i	0.971362	+	0.237606i
$5$	−1.15070	+	0.202899i	−0.514607	+	0.0907391i	−0.424920	−	0.905231i	$-0.639698\pi$
$5$	−1.15070	+	0.202899i	−0.514607	+	0.0907391i	−0.0896869	+	0.995970i	$0.528587\pi$
$6$	1.76797	−	3.48899i	0.721772	−	1.42438i
$7$	−2.48117	+	4.29751i	−0.937793	+	1.62431i	−0.168217	+	0.985750i	$0.553801\pi$
$7$	−2.48117	+	4.29751i	−0.937793	+	1.62431i	−0.769576	+	0.638555i	$0.779532\pi$
$8$	2.64726	+	0.995986i	0.935949	+	0.352134i
$9$	−3.56165	−	2.98858i	−1.18722	−	0.996194i
$10$	−1.64997	+	0.0901496i	−0.521767	+	0.0285078i
$11$	−1.12791	+	0.651199i	−0.340077	+	0.196344i	−0.660306	−	0.750996i	$-0.729574\pi$
$11$	−1.12791	+	0.651199i	−0.340077	+	0.196344i	0.320229	+	0.947340i	$0.396240\pi$
$12$	3.07276	−	4.59954i	0.887031	−	1.32777i
$13$	−1.56654	−	4.30402i	−0.434479	−	1.19372i	−0.943035	−	0.332693i	$-0.892043\pi$
$13$	−1.56654	−	4.30402i	−0.434479	−	1.19372i	0.508556	−	0.861029i	$-0.330179\pi$
$14$	−4.21095	+	5.61404i	−1.12542	+	1.50042i
$15$	−0.561168	+	3.18254i	−0.144893	+	0.821729i
$16$	3.54835	+	1.84641i	0.887087	+	0.461602i
$17$	2.55523	−	2.14409i	0.619734	−	0.520018i	−0.277986	−	0.960585i	$-0.589667\pi$
$17$	2.55523	−	2.14409i	0.619734	−	0.520018i	0.897720	+	0.440567i	$0.145222\pi$
$18$	−4.49499	−	4.79886i	−1.05948	−	1.13110i
$19$	−0.369712	+	4.34319i	−0.0848177	+	0.996396i
$19$	−0.369712	+	4.34319i	−0.0848177	+	0.996396i
$20$	−2.33190	−	0.152648i	−0.521430	−	0.0341331i
$21$	8.82201	+	10.5137i	1.92512	+	2.29427i
$22$	−1.69384	+	0.723442i	−0.361129	+	0.154238i
$23$	−0.0598623	+	0.339496i	−0.0124822	+	0.0707898i	−0.990413	−	0.138141i	$-0.955887\pi$
$23$	−0.0598623	+	0.339496i	−0.0124822	+	0.0707898i	0.977930	+	0.208931i	$0.0669984\pi$
$24$	5.09269	−	5.93799i	1.03954	−	1.21209i
$25$	−3.41553	+	1.24315i	−0.683106	+	0.248630i
$26$	−1.47113	−	6.30818i	−0.288513	−	1.23714i
$27$	−3.95069	+	2.28093i	−0.760310	+	0.438965i
$28$	−6.86245	+	7.16979i	−1.29688	+	1.35496i
$29$	0.903650	−	1.07693i	0.167804	−	0.199981i	−0.675589	−	0.737279i	$-0.736111\pi$
$29$	0.903650	−	1.07693i	0.167804	−	0.199981i	0.843392	+	0.537298i	$0.180555\pi$
$30$	−1.32649	+	4.37349i	−0.242182	+	0.798487i
$31$	2.59290	−	4.49103i	0.465698	−	0.806612i	−0.533535	−	0.845778i	$-0.679137\pi$
$31$	2.59290	−	4.49103i	0.465698	−	0.806612i	0.999233	+	0.0391657i	$0.0124700\pi$
$32$	4.66960	+	3.19294i	0.825476	+	0.564437i
$33$	0.625501	+	3.54739i	0.108886	+	0.617521i
$34$	3.95051	−	2.57800i	0.677508	−	0.442123i
$35$	1.98311	−	5.44855i	0.335207	−	0.920973i
$36$	−5.49910	−	7.49853i	−0.916516	−	1.24975i
$37$		−	3.14124i		−	0.516417i	−0.966089	−	0.258208i	$-0.916868\pi$
$37$		−	3.14124i		−	0.516417i	0.966089	−	0.258208i	$-0.0831321\pi$
$38$	−1.25409	+	6.03550i	−0.203440	+	0.979087i
$39$	−12.6678			−2.02848
$40$	−3.24828	−	0.608951i	−0.513598	−	0.0962835i
$41$	8.84858	+	3.22062i	1.38192	+	0.502976i	0.922758	−	0.385379i	$-0.125929\pi$
$41$	8.84858	+	3.22062i	1.38192	+	0.502976i	0.459157	+	0.888355i	$0.348151\pi$
$42$	10.6073	+	16.2547i	1.63675	+	2.50815i
$43$	−6.63623	+	1.17015i	−1.01202	+	0.178446i	−0.654981	−	0.755645i	$-0.727323\pi$
$43$	−6.63623	+	1.17015i	−1.01202	+	0.178446i	−0.357035	+	0.934091i	$0.616212\pi$
$44$	−2.50067	+	0.729103i	−0.376991	+	0.109916i
$45$	4.70476	+	2.71629i	0.701344	+	0.404921i
$46$	−0.141502	+	0.466539i	−0.0208634	+	0.0687875i
$47$	−0.689587	−	0.578632i	−0.100587	−	0.0844022i	0.591107	−	0.806593i	$-0.298691\pi$
$47$	−0.689587	−	0.578632i	−0.100587	−	0.0844022i	−0.691694	+	0.722191i	$0.743135\pi$
$48$	8.15528	−	7.47542i	1.17711	−	1.07898i
$49$	−8.81238	−	15.2635i	−1.25891	−	2.18050i
$50$	−5.00596	+	1.16744i	−0.707949	+	0.165101i
$51$	−3.15530	−	8.66913i	−0.441831	−	1.21392i
$52$	−0.998025	−	9.10596i	−0.138401	−	1.26277i
$53$	−1.26559	−	0.223157i	−0.173842	−	0.0306530i	0.0860497	−	0.996291i	$-0.472576\pi$
$53$	−1.26559	−	0.223157i	−0.173842	−	0.0306530i	−0.259891	+	0.965638i	$0.583687\pi$
$54$	−5.93297	+	2.53397i	−0.807374	+	0.344830i
$55$	1.16575	−	0.978183i	0.157190	−	0.131898i
$56$	−10.8486	+	8.90543i	−1.44970	+	1.19004i
$57$	10.9381	+	5.06928i	1.44878	+	0.671443i
$58$	1.45102	−	1.35914i	0.190528	−	0.178464i
$59$	−6.06841	−	7.23205i	−0.790040	−	0.941533i	0.209300	−	0.977851i	$-0.432881\pi$
$59$	−6.06841	−	7.23205i	−0.790040	−	0.941533i	−0.999340	+	0.0363185i	$0.988437\pi$
$60$	−2.60258	+	5.91613i	−0.335991	+	0.763769i
$61$	−2.91105	−	0.513296i	−0.372721	−	0.0657208i	−0.0158500	−	0.999874i	$-0.505045\pi$
$61$	−2.91105	−	0.513296i	−0.372721	−	0.0657208i	−0.356871	+	0.934154i	$0.616157\pi$
$62$	4.40057	−	5.86684i	0.558873	−	0.745090i
$63$	21.6805	−	7.89106i	2.73149	−	0.994180i
$64$	6.01602	+	5.27328i	0.752003	+	0.659160i
$65$	2.67589	+	4.63477i	0.331903	+	0.574873i
$66$	0.277915	+	5.08657i	0.0342090	+	0.626114i
$67$	−1.95759	+	2.33296i	−0.239157	+	0.285017i	−0.872251	−	0.489059i	$-0.837340\pi$
$67$	−1.95759	+	2.33296i	−0.239157	+	0.285017i	0.633094	+	0.774075i	$0.281785\pi$
$68$	5.98300	−	2.95110i	0.725545	−	0.357874i
$69$	0.825710	+	0.476724i	0.0994038	+	0.0573908i
$70$	3.70644	−	7.31445i	0.443004	−	0.874244i
$71$	1.96983	+	11.1714i	0.233775	+	1.32581i	0.845177	+	0.534486i	$0.179495\pi$
$71$	1.96983	+	11.1714i	0.233775	+	1.32581i	−0.611402	+	0.791320i	$0.709394\pi$
$72$	−6.45205	−	11.4589i	−0.760382	−	1.35045i
$73$	−1.39362	−	0.507236i	−0.163111	−	0.0593675i	0.259174	−	0.965831i	$-0.416550\pi$
$73$	−1.39362	−	0.507236i	−0.163111	−	0.0593675i	−0.422285	+	0.906463i	$0.638772\pi$
$74$	0.531588	−	4.41046i	0.0617958	−	0.512706i
$75$			10.0528i			1.16080i
$76$	−2.78218	+	8.26193i	−0.319138	+	0.947708i
$77$		−	6.46293i		−	0.736519i
$78$	−17.7863	−	2.14376i	−2.01390	−	0.242733i
$79$	8.75250	+	3.18565i	0.984733	+	0.358414i	0.783679	−	0.621166i	$-0.213341\pi$
$79$	8.75250	+	3.18565i	0.984733	+	0.358414i	0.201055	+	0.979580i	$0.435563\pi$
$80$	−4.45770	−	1.40470i	−0.498386	−	0.157050i
$81$	−0.231166	−	1.31101i	−0.0256852	−	0.145668i
$82$	11.8788	+	6.01935i	1.31180	+	0.664726i
$83$	11.1997	+	6.46616i	1.22933	+	0.709754i	0.966890	−	0.255195i	$-0.0821396\pi$
$83$	11.1997	+	6.46616i	1.22933	+	0.709754i	0.262440	+	0.964948i	$0.415473\pi$
$84$	12.1425	+	24.6175i	1.32486	+	2.68598i
$85$	−2.50526	+	2.98565i	−0.271733	+	0.323839i
$86$	−9.51564	+	0.519906i	−1.02610	+	0.0560629i
$87$	−1.94409	−	3.36726i	−0.208428	−	0.361009i
$88$	−3.63446	+	0.600514i	−0.387435	+	0.0640150i
$89$	2.44335	−	0.889305i	0.258994	−	0.0942661i	−0.209260	−	0.977860i	$-0.567105\pi$
$89$	2.44335	−	0.889305i	0.258994	−	0.0942661i	0.468254	+	0.883594i	$0.344883\pi$
$90$	6.14605	+	4.61000i	0.647851	+	0.485936i
$91$	22.3834	+	3.94680i	2.34642	+	0.413737i
$92$	−0.277628	+	0.631099i	−0.0289447	+	0.0657967i
$93$	−9.21927	−	10.9871i	−0.955994	−	1.13931i
$94$	−0.870295	−	0.929128i	−0.0897641	−	0.0958322i
$95$	−0.455802	−	5.07271i	−0.0467643	−	0.520449i
$96$	12.7155	−	9.11576i	1.29777	−	0.930374i
$97$	−2.82277	+	2.36859i	−0.286609	+	0.240493i	−0.774745	−	0.632274i	$-0.782122\pi$
$97$	−2.82277	+	2.36859i	−0.286609	+	0.240493i	0.488136	+	0.872768i	$0.337677\pi$
$98$	−9.79002	−	22.9220i	−0.988942	−	2.31548i
$99$	5.96338	+	1.05151i	0.599342	+	0.105680i
$100$	−7.22619	+	0.791999i	−0.722619	+	0.0791999i
$101$	−0.609616	−	1.67491i	−0.0606590	−	0.166659i	0.905661	−	0.424002i	$-0.139375\pi$
$101$	−0.609616	−	1.67491i	−0.0606590	−	0.166659i	−0.966320	+	0.257343i	$0.917153\pi$
$102$	−2.96315	−	12.7059i	−0.293395	−	1.25807i
$103$	−7.46400	−	12.9280i	−0.735450	−	1.27384i	−0.954526	−	0.298129i	$-0.903637\pi$
$103$	−7.46400	−	12.9280i	−0.735450	−	1.27384i	0.219076	−	0.975708i	$-0.429696\pi$
$104$	0.139711	−	12.9541i	0.0136998	−	1.27026i
$105$	−12.2847	−	10.3081i	−1.19886	−	1.00596i
$106$	−1.73918	−	0.527497i	−0.168924	−	0.0512350i
$107$	−6.27280	−	3.62160i	−0.606414	−	0.350114i	0.165146	−	0.986269i	$-0.447190\pi$
$107$	−6.27280	−	3.62160i	−0.606414	−	0.350114i	−0.771561	+	0.636156i	$0.780524\pi$
$108$	−8.75901	+	2.55380i	−0.842836	+	0.245740i
$109$	−0.818455	+	0.144316i	−0.0783937	+	0.0138229i	−0.212707	−	0.977116i	$-0.568228\pi$
$109$	−0.818455	+	0.144316i	−0.0783937	+	0.0138229i	0.134314	+	0.990939i	$0.457117\pi$
$110$	1.80231	−	1.17614i	0.171844	−	0.112141i
$111$	−8.16396	−	2.97144i	−0.774889	−	0.282036i
$112$	−16.7390	+	10.6678i	−1.58169	+	1.00801i
$113$	13.4059			1.26112			0.630559	−	0.776142i	$-0.282826\pi$
$113$	13.4059			1.26112			0.630559	+	0.776142i	$0.282826\pi$
$114$	14.4997	+	8.96857i	1.35802	+	0.839984i
$115$		−	0.402803i		−	0.0375615i
$116$	2.26731	−	1.66275i	0.210515	−	0.154382i
$117$	−7.28347	+	20.0112i	−0.673357	+	1.85003i
$118$	−7.29649	−	11.1811i	−0.671697	−	1.02931i
$119$	2.87430	+	16.3010i	0.263487	+	1.49431i
$120$	−4.65533	+	7.86612i	−0.424972	+	0.718075i
$121$	−4.65188	+	8.05729i	−0.422898	+	0.732481i
$122$	−4.00040	−	1.21333i	−0.362179	−	0.109849i
$123$	16.7405	−	19.9506i	1.50944	−	1.79888i
$124$	7.17147	−	7.49265i	0.644017	−	0.672860i
$125$	8.73753	−	5.04461i	0.781508	−	0.451204i
$126$	31.7760	−	7.41049i	2.83083	−	0.660179i
$127$	−10.7949	+	3.92901i	−0.957890	+	0.348643i	−0.773206	−	0.634155i	$-0.781348\pi$
$127$	−10.7949	+	3.92901i	−0.957890	+	0.348643i	−0.184684	+	0.982798i	$0.559126\pi$
$128$	7.55442	+	8.42204i	0.667723	+	0.744410i
$129$	−3.23634	+	18.3542i	−0.284944	+	1.61600i
$130$	2.97275	+	6.96030i	0.260727	+	0.610459i
$131$	10.5547	+	12.5786i	0.922165	+	1.09899i	0.994822	+	0.101637i	$0.0324080\pi$
$131$	10.5547	+	12.5786i	0.922165	+	1.09899i	−0.0726561	+	0.997357i	$0.523148\pi$
$132$	−0.470586	+	7.18884i	−0.0409593	+	0.625708i
$133$	−17.7476	−	12.3650i	−1.53891	−	1.07218i
$134$	−3.14336	+	2.94432i	−0.271545	+	0.254351i
$135$	4.08324	−	3.42624i	0.351429	−	0.294884i
$136$	8.89985	−	3.13100i	0.763156	−	0.268481i
$137$	0.745646	−	4.22877i	0.0637048	−	0.361288i	−0.936246	−	0.351346i	$-0.885724\pi$
$137$	0.745646	−	4.22877i	0.0637048	−	0.361288i	0.999951	−	0.00994210i	$-0.00316472\pi$
$138$	1.07866	+	0.809079i	0.0918220	+	0.0688734i
$139$	2.25049	+	6.18316i	0.190884	+	0.524449i	0.997806	−	0.0662092i	$-0.0210905\pi$
$139$	2.25049	+	6.18316i	0.190884	+	0.524449i	−0.806922	+	0.590658i	$0.798868\pi$
$140$	6.44185	−	9.64263i	0.544436	−	0.814951i
$141$	−2.15615	+	1.24486i	−0.181581	+	0.104836i
$142$	0.875211	+	16.0186i	0.0734461	+	1.34425i
$143$	4.56969	+	3.83442i	0.382136	+	0.320650i
$144$	−7.11984	−	17.1808i	−0.593320	−	1.43173i
$145$	−0.821319	+	1.42257i	−0.0682068	+	0.118138i
$146$	−1.87088	−	0.948027i	−0.154835	−	0.0784593i
$147$	−48.0053	+	8.46462i	−3.95941	+	0.698150i
$148$	1.49275	−	6.10256i	0.122704	−	0.501627i
$149$	−3.94197	+	10.8305i	−0.322938	+	0.887266i	0.666910	+	0.745138i	$0.267617\pi$
$149$	−3.94197	+	10.8305i	−0.322938	+	0.887266i	−0.989848	+	0.142128i	$0.954606\pi$
$150$	−1.70122	+	14.1146i	−0.138904	+	1.15245i
$151$	−13.0394			−1.06113			−0.530565	−	0.847644i	$-0.678020\pi$
$151$	−13.0394			−1.06113			−0.530565	+	0.847644i	$0.678020\pi$
$152$	−5.30448	+	11.1294i	−0.430250	+	0.902710i
$153$	−15.5086			−1.25380
$154$	1.09371	−	9.07429i	0.0881339	−	0.731227i
$155$	−2.07241	+	5.69390i	−0.166460	+	0.457345i
$156$	−24.6101	−	6.01991i	−1.97039	−	0.481978i
$157$	5.15855	−	0.909591i	0.411697	−	0.0725933i	0.0360361	−	0.999350i	$-0.488527\pi$
$157$	5.15855	−	0.909591i	0.411697	−	0.0725933i	0.375661	+	0.926757i	$0.377416\pi$
$158$	11.7499	+	5.95399i	0.934769	+	0.473674i
$159$	−1.77715	+	3.07811i	−0.140937	+	0.244110i
$160$	−6.02113	−	2.72664i	−0.476012	−	0.215560i
$161$	−1.31046	−	1.09960i	−0.103279	−	0.0866610i
$162$	−0.102709	−	1.87985i	−0.00806960	−	0.147695i
$163$	−5.65780	+	3.26653i	−0.443153	+	0.255855i	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−5.65780	+	3.26653i	−0.443153	+	0.255855i	0.261781	+	0.965127i	$0.415690\pi$
$164$	15.6599	+	10.4617i	1.22283	+	0.816923i
$165$	−1.43952	−	3.95505i	−0.112067	−	0.307900i
$166$	14.6307	+	10.9741i	1.13557	+	0.851759i
$167$	4.19049	−	23.7655i	0.324270	−	1.83903i	−0.190485	−	0.981690i	$-0.561006\pi$
$167$	4.19049	−	23.7655i	0.324270	−	1.83903i	0.514755	−	0.857337i	$-0.327883\pi$
$168$	12.8827	+	36.6190i	0.993924	+	2.82522i
$169$	−6.11201	+	5.12858i	−0.470154	+	0.394506i
$170$	−4.02277	+	3.76804i	−0.308532	+	0.288996i
$171$	14.2968	−	14.3640i	1.09330	−	1.09844i
$172$	−13.4484	−	0.880343i	−1.02543	−	0.0671255i
$173$	2.33887	+	2.78736i	0.177821	+	0.211919i	0.847592	−	0.530649i	$-0.178052\pi$
$173$	2.33887	+	2.78736i	0.177821	+	0.211919i	−0.669770	+	0.742568i	$0.733607\pi$
$174$	−2.15977	−	5.05681i	−0.163732	−	0.383356i
$175$	3.13205	−	17.7627i	0.236761	−	1.34274i
$176$	−5.20459	+	0.228097i	−0.392311	+	0.0171935i
$177$	−24.5362	+	8.93045i	−1.84425	+	0.671253i
$178$	3.58108	−	0.835146i	0.268413	−	0.0625969i
$179$	1.74136	−	1.00537i	0.130155	−	0.0751451i	−0.433509	−	0.901149i	$-0.642725\pi$
$179$	1.74136	−	1.00537i	0.130155	−	0.0751451i	0.563664	+	0.826004i	$0.309391\pi$
$180$	7.84923	+	7.51276i	0.585047	+	0.559968i
$181$	−1.34743	+	1.60581i	−0.100154	+	0.119359i	−0.813793	−	0.581155i	$-0.802601\pi$
$181$	−1.34743	+	1.60581i	−0.100154	+	0.119359i	0.713639	+	0.700513i	$0.247046\pi$
$182$	30.7596	+	9.32943i	2.28005	+	0.691543i
$183$	−4.08772	+	7.08015i	−0.302173	+	0.523380i
$184$	−0.496605	+	0.839114i	−0.0366102	+	0.0618603i
$185$	0.637354	+	3.61461i	0.0468592	+	0.265752i
$186$	−11.0850	−	16.9866i	−0.812792	−	1.24552i
$187$	−1.48584	+	4.08230i	−0.108655	+	0.298527i
$188$	−1.06470	−	1.45182i	−0.0776516	−	0.105885i
$189$		−	22.6375i		−	1.64663i
$190$	0.218478	−	7.19948i	0.0158500	−	0.522305i
$191$	−3.51547			−0.254371			−0.127185	−	0.991879i	$-0.540594\pi$
$191$	−3.51547			−0.254371			−0.127185	+	0.991879i	$0.540594\pi$
$192$	19.3959	−	10.6472i	1.39978	−	0.768394i
$193$	7.50594	+	2.73194i	0.540290	+	0.196649i	0.597727	−	0.801700i	$-0.296071\pi$
$193$	7.50594	+	2.73194i	0.540290	+	0.196649i	−0.0574374	+	0.998349i	$0.518293\pi$
$194$	−4.36415	+	2.84792i	−0.313328	+	0.204469i
$195$	14.5768	−	2.57029i	1.04387	−	0.184062i
$196$	−9.86663	−	33.8405i	−0.704759	−	2.41718i
$197$	13.7278	+	7.92577i	0.978068	+	0.564688i	0.901686	−	0.432391i	$-0.142330\pi$
$197$	13.7278	+	7.92577i	0.978068	+	0.564688i	0.0763820	+	0.997079i	$0.475663\pi$
$198$	8.19495	+	2.48554i	0.582390	+	0.176640i
$199$	12.9867	+	10.8972i	0.920606	+	0.772480i	0.974107	−	0.226088i	$-0.0725935\pi$
$199$	12.9867	+	10.8972i	0.920606	+	0.772480i	−0.0535009	+	0.998568i	$0.517038\pi$
$200$	−10.2800	−	0.110870i	−0.726904	−	0.00783969i
$201$	4.21151	+	7.29455i	0.297057	+	0.514518i
$202$	−0.572490	−	2.45482i	−0.0402803	−	0.172720i
$203$	2.38600	+	6.55548i	0.167464	+	0.460105i
$204$	−2.01021	−	18.3412i	−0.140743	−	1.28414i
$205$	−10.8355	−	1.91059i	−0.756783	−	0.133441i
$206$	−8.29205	−	19.4147i	−0.577735	−	1.35269i
$207$	1.22782	−	1.03026i	0.0853394	−	0.0716082i
$208$	2.38837	−	18.1646i	0.165604	−	1.25949i
$209$	−2.41128	−	5.13948i	−0.166792	−	0.355505i
$210$	−15.5039	−	16.5520i	−1.06987	−	1.14219i
$211$	3.93730	+	4.69230i	0.271055	+	0.323031i	0.884351	−	0.466822i	$-0.154601\pi$
$211$	3.93730	+	4.69230i	0.271055	+	0.323031i	−0.613296	+	0.789853i	$0.710157\pi$
$212$	−2.35264	−	1.03495i	−0.161580	−	0.0710809i
$213$	30.8975	+	5.44806i	2.11706	+	0.373295i
$214$	−8.19446	−	6.14646i	−0.560162	−	0.420163i
$215$	7.39886	−	2.69297i	0.504598	−	0.183659i
$216$	−12.7303	+	2.10340i	−0.866186	+	0.143118i
$217$	12.8668	+	22.2860i	0.873457	+	1.51287i
$218$	−1.17358	+	0.0641207i	−0.0794845	+	0.00434280i
$219$	−2.63658	+	3.14215i	−0.178163	+	0.212327i
$220$	2.72958	−	1.34636i	0.184028	−	0.0907716i
$221$	−13.2311	−	7.63897i	−0.890018	−	0.513852i
$222$	−10.9598	−	5.55363i	−0.735572	−	0.372735i
$223$	0.479933	+	2.72184i	0.0321387	+	0.182268i	0.996651	−	0.0817692i	$-0.0260570\pi$
$223$	0.479933	+	2.72184i	0.0321387	+	0.182268i	−0.964513	+	0.264037i	$0.914946\pi$
$224$	−25.3077	+	12.1454i	−1.69094	+	0.811501i
$225$	15.8802	+	5.77992i	1.05868	+	0.385328i
$226$	18.8225	+	2.26866i	1.25206	+	0.150909i
$227$		−	22.8081i		−	1.51383i	−0.653516	−	0.756913i	$-0.726707\pi$
$227$		−	22.8081i		−	1.51383i	0.653516	−	0.756913i	$-0.273293\pi$
$228$	18.8406	+	15.0461i	1.24775	+	0.996453i
$229$			20.0645i			1.32590i	0.748665	+	0.662948i	$0.230695\pi$
$229$			20.0645i			1.32590i	−0.748665	+	0.662948i	$0.769305\pi$
$230$	0.0681657	−	0.565556i	0.00449472	−	0.0372916i
$231$	−16.7969	−	6.11357i	−1.10516	−	0.402244i
$232$	3.46481	−	1.95089i	0.227476	−	0.128082i
$233$	−4.22236	−	23.9462i	−0.276616	−	1.56877i	−0.733780	−	0.679387i	$-0.762246\pi$
$233$	−4.22236	−	23.9462i	−0.276616	−	1.56877i	0.457164	−	0.889382i	$-0.348865\pi$
$234$	−13.6128	+	26.8641i	−0.889898	+	1.75616i
$235$	0.910909	+	0.525914i	0.0594212	+	0.0343068i
$236$	−8.35249	−	16.9337i	−0.543701	−	1.10229i
$237$	16.5588	−	19.7340i	1.07561	−	1.28186i
$238$	1.27708	+	23.3738i	0.0827805	+	1.51510i
$239$	0.645825	+	1.11860i	0.0417749	+	0.0723563i	0.886157	−	0.463385i	$-0.153365\pi$
$239$	0.645825	+	1.11860i	0.0417749	+	0.0723563i	−0.844382	+	0.535742i	$0.820032\pi$
$240$	−7.86750	+	10.2566i	−0.507845	+	0.662062i
$241$	−11.7717	+	4.28456i	−0.758284	+	0.275993i	−0.692087	−	0.721814i	$-0.743309\pi$
$241$	−11.7717	+	4.28456i	−0.758284	+	0.275993i	−0.0661966	+	0.997807i	$0.521086\pi$
$242$	−7.89501	+	10.5256i	−0.507510	+	0.676613i
$243$	−17.1036	−	3.01582i	−1.09720	−	0.193465i
$244$	−5.41143	−	2.38056i	−0.346432	−	0.152399i
$245$	13.2373	+	15.7756i	0.845701	+	1.00787i
$246$	26.8808	−	25.1787i	1.71386	−	1.60533i
$247$	19.2724	−	5.21252i	1.22627	−	0.331665i
$248$	11.3371	−	9.30645i	0.719906	−	0.590960i
$249$	27.3996	−	22.9910i	1.73638	−	1.45700i
$250$	13.1216	−	5.60426i	0.829885	−	0.354445i
$251$	−23.1578	−	4.08335i	−1.46171	−	0.257739i	−0.614466	−	0.788943i	$-0.710629\pi$
$251$	−23.1578	−	4.08335i	−1.46171	−	0.257739i	−0.847244	+	0.531204i	$0.821740\pi$
$252$	45.8692	−	5.02732i	2.88949	−	0.316691i
$253$	−0.153560	−	0.421903i	−0.00965424	−	0.0265248i
$254$	−15.8215	+	3.68974i	−0.992727	+	0.231515i
$255$	5.38975	+	9.33532i	0.337519	+	0.584601i
$256$	9.18155	+	13.1034i	0.573847	+	0.818963i
$257$	2.46894	+	2.07168i	0.154008	+	0.129228i	0.716536	−	0.697550i	$-0.245727\pi$
$257$	2.46894	+	2.07168i	0.154008	+	0.129228i	−0.562528	+	0.826778i	$0.690171\pi$
$258$	−7.65005	+	25.2226i	−0.476271	+	1.57029i
$259$	13.4995	+	7.79394i	0.838818	+	0.484292i
$260$	2.99601	+	10.2757i	0.185805	+	0.637272i
$261$	−6.43697	+	1.13501i	−0.398439	+	0.0702555i
$262$	12.6906	+	19.4471i	0.784031	+	1.20145i
$263$	17.7478	+	6.45968i	1.09438	+	0.398321i	0.825241	−	0.564781i	$-0.191039\pi$
$263$	17.7478	+	6.45968i	1.09438	+	0.398321i	0.269137	+	0.963102i	$0.413261\pi$
$264$	−1.87729	+	10.0139i	−0.115539	+	0.616311i
$265$	1.50158			0.0922415
$266$	−22.8260	−	20.3645i	−1.39955	−	1.24863i
$267$		−	7.19139i		−	0.440106i
$268$	−4.91170	+	3.60203i	−0.300030	+	0.220029i
$269$	−7.48044	+	20.5523i	−0.456090	+	1.25310i	0.472283	+	0.881447i	$0.343430\pi$
$269$	−7.48044	+	20.5523i	−0.456090	+	1.25310i	−0.928373	+	0.371650i	$0.878792\pi$
$270$	6.31290	−	4.11962i	0.384191	−	0.250712i
$271$	−0.754137	−	4.27693i	−0.0458106	−	0.259805i	0.953297	−	0.302033i	$-0.0976654\pi$
$271$	−0.754137	−	4.27693i	−0.0458106	−	0.259805i	−0.999108	+	0.0422285i	$0.986554\pi$
$272$	13.0257	−	2.88998i	0.789799	−	0.175231i
$273$	31.4310	−	54.4402i	1.90229	−	3.29487i
$274$	1.76255	−	5.81122i	0.106480	−	0.351069i
$275$	3.04287	−	3.62635i	0.183492	−	0.218677i
$276$	1.37758	+	1.31853i	0.0829207	+	0.0793662i
$277$	22.6098	−	13.0538i	1.35849	−	0.784327i	0.369073	−	0.929400i	$-0.379675\pi$
$277$	22.6098	−	13.0538i	1.35849	−	0.784327i	0.989421	+	0.145074i	$0.0463420\pi$
$278$	2.11343	+	9.06232i	0.126755	+	0.543522i
$279$	−22.6568	+	8.24640i	−1.35643	+	0.493699i
$280$	10.6765	−	12.4486i	0.638043	−	0.743947i
$281$	0.552605	−	3.13398i	0.0329657	−	0.186957i	−0.963878	−	0.266343i	$-0.914185\pi$
$281$	0.552605	−	3.13398i	0.0329657	−	0.186957i	0.996844	+	0.0793854i	$0.0252958\pi$
$282$	−3.23802	+	1.38296i	−0.192821	+	0.0823540i
$283$	−6.83573	−	8.14651i	−0.406342	−	0.484260i	0.523601	−	0.851964i	$-0.324588\pi$
$283$	−6.83573	−	8.14651i	−0.406342	−	0.484260i	−0.929943	+	0.367704i	$0.880144\pi$
$284$	−1.48197	+	22.6391i	−0.0879388	+	1.34338i
$285$	−13.6149	−	3.61389i	−0.806479	−	0.214068i
$286$	5.76718	+	6.15705i	0.341021	+	0.364074i
$287$	−35.7954	+	30.0359i	−2.11294	+	1.77297i
$288$	−7.08914	−	25.3276i	−0.417732	−	1.49244i
$289$	−1.01995	+	5.78445i	−0.0599974	+	0.340262i
$290$	−1.39391	+	1.85837i	−0.0818534	+	0.109127i
$291$	3.48568	+	9.57682i	0.204334	+	0.561403i
$292$	−2.46637	−	1.64768i	−0.144334	−	0.0964235i
$293$	−21.9095	+	12.6495i	−1.27997	+	0.738990i	−0.976842	−	0.213960i	$-0.931364\pi$
$293$	−21.9095	+	12.6495i	−1.27997	+	0.738990i	−0.303126	+	0.952950i	$0.598030\pi$
$294$	−68.8343	+	3.76090i	−4.01450	+	0.219340i
$295$	8.45027	+	7.09062i	0.491994	+	0.412832i
$296$	3.12863	−	8.31569i	0.181848	−	0.483340i
$297$	2.97068	−	5.14536i	0.172376	−	0.298564i
$298$	−7.36755	+	14.5394i	−0.426791	+	0.842247i
$299$	1.55498	−	0.274184i	0.0899265	−	0.0158565i
$300$	−4.77720	+	19.5298i	−0.275812	+	1.12755i
$301$	11.4369	−	31.4226i	0.659211	−	1.81117i
$302$	−18.3080	−	2.20664i	−1.05351	−	0.126978i
$303$	−4.92968			−0.283203
$304$	−9.33118	+	14.7285i	−0.535180	+	0.844738i
$305$	3.45388			0.197768
$306$	−21.7749	−	2.62450i	−1.24479	−	0.150033i
$307$	1.34290	−	3.68958i	0.0766431	−	0.210575i	−0.895454	−	0.445154i	$-0.853149\pi$
$307$	1.34290	−	3.68958i	0.0766431	−	0.210575i	0.972097	+	0.234579i	$0.0753711\pi$
$308$	3.07126	−	12.5557i	0.175001	−	0.715427i
$309$	−40.6600	+	7.16945i	−2.31307	+	0.407856i
$310$	−3.87334	+	7.64382i	−0.219991	+	0.434140i
$311$	2.32265	−	4.02294i	0.131705	−	0.228120i	−0.792629	−	0.609705i	$-0.791288\pi$
$311$	2.32265	−	4.02294i	0.131705	−	0.228120i	0.924334	+	0.381584i	$0.124621\pi$
$312$	−33.5351	−	12.6170i	−1.89855	−	0.714297i
$313$	−15.0484	−	12.6271i	−0.850584	−	0.713725i	0.109334	−	0.994005i	$-0.465128\pi$
$313$	−15.0484	−	12.6271i	−0.850584	−	0.713725i	−0.959918	+	0.280280i	$0.909573\pi$
$314$	7.39680	−	0.404139i	0.417425	−	0.0228069i
$315$	−23.3466	+	13.4792i	−1.31543	+	0.759465i
$316$	15.4898	+	10.3481i	0.871371	+	0.582128i
$317$	−8.18980	−	22.5013i	−0.459985	−	1.26380i	−0.925496	−	0.378757i	$-0.876352\pi$
$317$	−8.18980	−	22.5013i	−0.459985	−	1.26380i	0.465511	−	0.885042i	$-0.345870\pi$
$318$	−3.01611	+	4.02109i	−0.169135	+	0.225491i
$319$	−0.317941	+	1.80313i	−0.0178013	+	0.100956i
$320$	−7.99255	−	4.84730i	−0.446797	−	0.270972i
$321$	−15.3461	+	12.8769i	−0.856537	+	0.718720i
$322$	−1.65387	−	1.76567i	−0.0921664	−	0.0983969i
$323$	8.36750	+	11.8905i	0.465580	+	0.661607i
$324$	0.173915	−	2.65678i	0.00966193	−	0.147599i
$325$	10.7011	+	12.7531i	0.593591	+	0.707414i
$326$	−8.49664	+	3.62892i	−0.470585	+	0.200987i
$327$	−0.399142	+	2.26365i	−0.0220726	+	0.125180i
$328$	20.2168	+	17.3389i	1.11629	+	0.957380i
$329$	4.19766	−	1.52782i	0.231424	−	0.0842316i
$330$	−1.35185	−	5.79671i	−0.0744172	−	0.319098i
$331$	7.14279	−	4.12389i	0.392603	−	0.226669i	−0.290684	−	0.956819i	$-0.593883\pi$
$331$	7.14279	−	4.12389i	0.392603	−	0.226669i	0.683287	+	0.730150i	$0.260550\pi$
$332$	18.6852	+	17.8842i	1.02548	+	0.981523i
$333$	−9.38785	+	11.1880i	−0.514451	+	0.613099i
$334$	9.90547	−	32.6588i	0.542003	−	1.78701i
$335$	1.77923	−	3.08172i	0.0972099	−	0.168372i
$336$	11.8910	+	53.5952i	0.648709	+	2.92386i
$337$	−1.53286	−	8.69330i	−0.0835004	−	0.473554i	−0.997670	−	0.0682227i	$-0.978267\pi$
$337$	−1.53286	−	8.69330i	−0.0835004	−	0.473554i	0.914170	−	0.405332i	$-0.132844\pi$
$338$	−9.44948	+	6.16647i	−0.513984	+	0.335412i
$339$	12.6812	−	34.8413i	0.688748	−	1.89232i
$340$	−6.28584	+	4.60976i	−0.340897	+	0.249999i
$341$			6.75396i			0.365748i
$342$	22.5042	−	17.7484i	1.21689	−	0.959724i
$343$	52.7237			2.84681
$344$	−18.7333	−	3.51191i	−1.01003	−	0.189349i
$345$	−1.04687	−	0.381029i	−0.0563615	−	0.0205139i
$346$	2.81220	+	4.30940i	0.151185	+	0.231675i
$347$	−26.0874	+	4.59991i	−1.40044	+	0.246936i	−0.822326	−	0.569017i	$-0.807324\pi$
$347$	−26.0874	+	4.59991i	−1.40044	+	0.246936i	−0.578118	+	0.815953i	$0.696213\pi$
$348$	−2.17667	−	7.46552i	−0.116682	−	0.400194i
$349$	2.51203	+	1.45032i	0.134466	+	0.0776340i	0.565724	−	0.824595i	$-0.308597\pi$
$349$	2.51203	+	1.45032i	0.134466	+	0.0776340i	−0.431258	+	0.902229i	$0.641930\pi$
$350$	7.40352	−	24.4098i	0.395735	−	1.30476i
$351$	16.0061	+	13.4307i	0.854341	+	0.716877i
$352$	−7.34612	−	0.560506i	−0.391550	−	0.0298751i
$353$	16.4834	+	28.5502i	0.877325	+	1.51957i	0.854265	+	0.519837i	$0.174007\pi$
$353$	16.4834	+	28.5502i	0.877325	+	1.51957i	0.0230598	+	0.999734i	$0.492659\pi$
$354$	−35.9614	+	8.38658i	−1.91133	+	0.445742i
$355$	−4.53334	−	12.4553i	−0.240605	−	0.661056i
$356$	5.16935	−	0.566568i	0.273975	−	0.0300280i
$357$	45.0845	+	7.94961i	2.38612	+	0.420738i
$358$	2.61509	−	1.11691i	0.138212	−	0.0590304i
$359$	4.21223	−	3.53448i	0.222313	−	0.186543i	−0.524828	−	0.851208i	$-0.675870\pi$
$359$	4.21223	−	3.53448i	0.222313	−	0.186543i	0.747141	+	0.664665i	$0.231426\pi$
$360$	9.74935	+	11.8766i	0.513836	+	0.625953i
$361$	−18.7266	−	3.21146i	−0.985612	−	0.169024i
$362$	−2.16361	+	2.02661i	−0.113717	+	0.106516i
$363$	16.5402	+	19.7118i	0.868134	+	1.03460i
$364$	41.6092	+	18.3044i	2.18092	+	0.959411i
$365$	1.70655	+	0.300911i	0.0893250	+	0.0157504i
$366$	−6.93754	+	9.24913i	−0.362631	+	0.483460i
$367$	−14.4092	+	5.24452i	−0.752154	+	0.273762i	−0.689512	−	0.724274i	$-0.742175\pi$
$367$	−14.4092	+	5.24452i	−0.752154	+	0.273762i	−0.0626421	+	0.998036i	$0.519953\pi$
$368$	−0.839261	+	1.09412i	−0.0437495	+	0.0570349i
$369$	−21.8905	−	37.9154i	−1.13957	−	1.97380i
$370$	0.283182	+	5.18296i	0.0147219	+	0.269449i
$371$	4.09915	−	4.88517i	0.212817	−	0.253626i
$372$	−12.6893	−	25.7260i	−0.657909	−	1.33383i
$373$	4.42487	+	2.55470i	0.229111	+	0.132277i	0.610162	−	0.792277i	$-0.291104\pi$
$373$	4.42487	+	2.55470i	0.229111	+	0.132277i	−0.381051	+	0.924554i	$0.624438\pi$
$374$	−2.77703	+	5.48032i	−0.143597	+	0.283380i
$375$	−4.84554	−	27.4804i	−0.250223	−	1.41908i
$376$	−1.24921	−	2.21861i	−0.0644231	−	0.114416i
$377$	−6.05073	−	2.20228i	−0.311628	−	0.113423i
$378$	3.83091	−	31.7842i	0.197041	−	1.63480i
$379$			36.8883i			1.89483i	0.320014	+	0.947413i	$0.396312\pi$
$379$			36.8883i			1.89483i	−0.320014	+	0.947413i	$0.603688\pi$
$380$	1.52511	−	10.0715i	0.0782366	−	0.516655i
$381$			31.7721i			1.62773i
$382$	−4.93590	−	0.594918i	−0.252543	−	0.0304387i
$383$	−29.7129	−	10.8146i	−1.51826	−	0.552600i	−0.557544	−	0.830147i	$-0.688256\pi$
$383$	−29.7129	−	10.8146i	−1.51826	−	0.552600i	−0.960712	+	0.277547i	$0.910479\pi$
$384$	29.0346	−	11.6669i	1.48167	−	0.595372i
$385$	1.31132	+	7.43687i	0.0668311	+	0.379018i
$386$	10.0764	+	5.10601i	0.512876	+	0.259889i
$387$	27.1330	+	15.6653i	1.37925	+	0.796310i
$388$	−6.60944	+	3.26009i	−0.335544	+	0.165506i
$389$	−3.66036	+	4.36225i	−0.185588	+	0.221175i	−0.850814	−	0.525467i	$-0.823891\pi$
$389$	−3.66036	+	4.36225i	−0.185588	+	0.221175i	0.665226	+	0.746642i	$0.268335\pi$
$390$	20.9016	−	1.14200i	1.05839	−	0.0578275i
$391$	0.574948	+	0.995840i	0.0290764	+	0.0503618i
$392$	−8.12648	−	49.1835i	−0.410449	−	2.48414i
$393$	42.6753	−	15.5325i	2.15268	−	0.783513i
$394$	17.9333	+	13.4513i	0.903468	+	0.677669i
$395$	−10.7178	−	1.88984i	−0.539273	−	0.0950883i
$396$	11.0855	+	4.87665i	0.557068	+	0.245061i
$397$	−5.48790	−	6.54022i	−0.275430	−	0.328244i	0.610542	−	0.791984i	$-0.290952\pi$
$397$	−5.48790	−	6.54022i	−0.275430	−	0.328244i	−0.885972	+	0.463740i	$0.846507\pi$
$398$	16.3900	+	17.4979i	0.821554	+	0.877092i
$399$	−48.9244	+	34.4286i	−2.44929	+	1.72359i
$400$	−14.4149	−	1.89533i	−0.720743	−	0.0947667i
$401$	−11.0246	+	9.25072i	−0.550541	+	0.461959i	−0.875124	−	0.483898i	$-0.839220\pi$
$401$	−11.0246	+	9.25072i	−0.550541	+	0.461959i	0.324583	+	0.945857i	$0.394776\pi$
$402$	4.67873	+	10.9546i	0.233354	+	0.546367i
$403$	−23.3914	−	4.12453i	−1.16521	−	0.205457i
$404$	−0.388380	−	3.54357i	−0.0193226	−	0.176299i
$405$	0.532004	+	1.46167i	0.0264355	+	0.0726310i
$406$	2.24069	+	9.60802i	0.111204	+	0.476838i
$407$	2.04557	+	3.54303i	0.101395	+	0.175622i
$408$	0.281404	−	26.0921i	0.0139316	−	1.29175i
$409$	−12.0820	−	10.1380i	−0.597414	−	0.501290i	0.293199	−	0.956051i	$-0.405280\pi$
$409$	−12.0820	−	10.1380i	−0.597414	−	0.501290i	−0.890613	+	0.454761i	$0.849725\pi$
$410$	−14.8903	−	4.51624i	−0.735377	−	0.223041i
$411$	−10.2851	−	5.93808i	−0.507324	−	0.292904i
$412$	−8.35694	−	28.6626i	−0.411717	−	1.41210i
$413$	46.1365	−	8.13512i	2.27023	−	0.400303i
$414$	1.89827	−	1.23876i	0.0932950	−	0.0608818i
$415$	−14.1995	−	5.16818i	−0.697024	−	0.253696i
$416$	6.42738	−	25.0999i	0.315128	−	1.23062i
$417$	18.1986			0.891190
$418$	−2.51581	−	7.62416i	−0.123052	−	0.372910i
$419$		−	23.7276i		−	1.15917i	−0.814911	−	0.579586i	$-0.803214\pi$
$419$		−	23.7276i		−	1.15917i	0.814911	−	0.579586i	$-0.196786\pi$
$420$	−18.9672	−	25.8635i	−0.925504	−	1.26201i
$421$	10.8769	−	29.8841i	0.530109	−	1.45646i	−0.328833	−	0.944388i	$-0.606655\pi$
$421$	10.8769	−	29.8841i	0.530109	−	1.45646i	0.858942	−	0.512073i	$-0.171122\pi$
$422$	4.73411	+	7.25453i	0.230453	+	0.353145i
$423$	0.726780	+	4.12178i	0.0353373	+	0.200408i
$424$	−3.12808	−	1.85126i	−0.151913	−	0.0899052i
$425$	−6.06203	+	10.4997i	−0.294052	+	0.509312i
$426$	42.4597	+	12.8781i	2.05718	+	0.623946i
$427$	9.42869	−	11.2367i	0.456286	−	0.543781i
$428$	−10.4653	−	10.0167i	−0.505859	−	0.484174i
$429$	14.2882	−	8.24929i	0.689840	−	0.398279i
$430$	10.8441	−	2.52896i	0.522950	−	0.121958i
$431$	8.05218	−	2.93076i	0.387860	−	0.141170i	−0.140727	−	0.990048i	$-0.544944\pi$
$431$	8.05218	−	2.93076i	0.387860	−	0.141170i	0.528587	+	0.848879i	$0.322722\pi$
$432$	−18.2299	+	0.798948i	−0.877088	+	0.0384394i
$433$	−0.880426	+	4.99314i	−0.0423106	+	0.239955i	−0.998627	−	0.0523771i	$-0.983320\pi$
$433$	−0.880426	+	4.99314i	−0.0423106	+	0.239955i	0.956317	+	0.292332i	$0.0944313\pi$
$434$	14.2943	+	33.4681i	0.686146	+	1.60652i
$435$	2.92027	+	3.48024i	0.140016	+	0.166865i
$436$	−1.65861	−	0.108574i	−0.0794331	−	0.00519974i
$437$	−1.45236	−	0.385509i	−0.0694760	−	0.0184414i
$438$	−4.23363	+	3.96555i	−0.202291	+	0.189482i
$439$	20.5125	−	17.2120i	0.979009	−	0.821486i	−0.00493087	−	0.999988i	$-0.501570\pi$
$439$	20.5125	−	17.2120i	0.979009	−	0.821486i	0.983940	+	0.178502i	$0.0571251\pi$
$440$	4.06031	−	1.42844i	0.193568	−	0.0680980i
$441$	−14.2296	+	80.6998i	−0.677598	+	3.84285i
$442$	−17.2844	−	12.9646i	−0.822134	−	0.616662i
$443$	−10.8240	−	29.7386i	−0.514262	−	1.41292i	−0.876755	−	0.480937i	$-0.840297\pi$
$443$	−10.8240	−	29.7386i	−0.514262	−	1.41292i	0.362493	−	0.931986i	$-0.381926\pi$
$444$	−14.4483	−	9.65229i	−0.685684	−	0.458077i
$445$	−2.63111	+	1.51907i	−0.124727	+	0.0720109i
$446$	0.213239	+	3.90282i	0.0100971	+	0.184804i
$447$	24.4191	+	20.4900i	1.15498	+	0.969145i
$448$	−37.5887	+	12.7700i	−1.77590	+	0.603327i
$449$	−3.24728	+	5.62445i	−0.153249	+	0.265434i	−0.932420	−	0.361377i	$-0.882307\pi$
$449$	−3.24728	+	5.62445i	−0.153249	+	0.265434i	0.779171	+	0.626811i	$0.215640\pi$
$450$	21.3185	+	10.8027i	1.00496	+	0.509243i
$451$	−12.0777	+	2.12962i	−0.568715	+	0.100280i
$452$	26.0439	+	6.37062i	1.22500	+	0.299649i
$453$	−12.3345	+	33.8888i	−0.579527	+	1.59224i
$454$	3.85978	−	32.0237i	0.181149	−	1.50295i
$455$	−26.5573			−1.24503
$456$	23.9070	+	24.3139i	1.11955	+	1.13860i
$457$	7.53719			0.352575			0.176288	−	0.984339i	$-0.443591\pi$
$457$	7.53719			0.352575			0.176288	+	0.984339i	$0.443591\pi$
$458$	−3.39548	+	28.1715i	−0.158660	+	1.31637i
$459$	−5.20438	+	14.2989i	−0.242920	+	0.667416i
$460$	0.191416	−	0.782534i	0.00892484	−	0.0364858i
$461$	−12.6565	+	2.23168i	−0.589470	+	0.103939i	−0.460424	−	0.887699i	$-0.652303\pi$
$461$	−12.6565	+	2.23168i	−0.589470	+	0.103939i	−0.129046	+	0.991639i	$0.541192\pi$
$462$	−22.5491	−	11.4263i	−1.04908	−	0.531599i
$463$	5.80079	−	10.0473i	0.269586	−	0.466936i	−0.699169	−	0.714956i	$-0.746447\pi$
$463$	5.80079	−	10.0473i	0.269586	−	0.466936i	0.968755	+	0.248020i	$0.0797800\pi$
$464$	5.19491	−	2.15281i	0.241168	−	0.0999416i
$465$	12.8378	+	10.7722i	0.595341	+	0.499550i
$466$	−1.87603	−	34.3363i	−0.0869055	−	1.59060i
$467$	−12.7970	+	7.38834i	−0.592174	+	0.341892i	−0.765957	−	0.642892i	$-0.777734\pi$
$467$	−12.7970	+	7.38834i	−0.592174	+	0.341892i	0.173783	+	0.984784i	$0.444401\pi$
$468$	−23.6593	+	35.4150i	−1.09365	+	1.63706i
$469$	−5.16882	−	14.2012i	−0.238674	−	0.655751i
$470$	1.18996	+	0.892562i	0.0548889	+	0.0411708i
$471$	2.51571	−	14.2673i	0.115918	−	0.657402i
$472$	−8.86167	−	25.1892i	−0.407891	−	1.15943i
$473$	6.72307	−	5.64133i	0.309127	−	0.259388i
$474$	26.5889	−	24.9053i	1.22127	−	1.14394i
$475$	−4.13648	−	15.2939i	−0.189795	−	0.701733i
$476$	−2.16244	+	33.0342i	−0.0991151	+	1.51412i
$477$	3.84065	+	4.57711i	0.175851	+	0.209572i
$478$	0.717472	+	1.67987i	0.0328164	+	0.0768353i
$479$	5.48085	−	31.0835i	0.250427	−	1.42024i	−0.557118	−	0.830433i	$-0.688093\pi$
$479$	5.48085	−	31.0835i	0.250427	−	1.42024i	0.807545	−	0.589806i	$-0.200796\pi$
$480$	−12.7821	+	13.0694i	−0.583420	+	0.596535i
$481$	−13.5200	+	4.92087i	−0.616458	+	0.224372i
$482$	−17.2532	+	4.02363i	−0.785861	+	0.183271i
$483$	−4.09745	+	2.36566i	−0.186440	+	0.107641i
$484$	−12.8662	+	13.4425i	−0.584829	+	0.611021i
$485$	2.76757	−	3.29826i	0.125669	−	0.149766i
$486$	−23.5040	−	7.12879i	−1.06616	−	0.323369i
$487$	−7.17526	+	12.4279i	−0.325142	+	0.563162i	−0.981541	−	0.191252i	$-0.938745\pi$
$487$	−7.17526	+	12.4279i	−0.325142	+	0.563162i	0.656399	+	0.754414i	$0.272079\pi$
$488$	−7.19508	−	4.25819i	−0.325706	−	0.192759i
$489$	3.13763	+	17.7944i	0.141888	+	0.804689i
$490$	15.9162	+	24.3899i	0.719020	+	1.10182i
$491$	7.33922	−	20.1643i	0.331214	−	0.910004i	−0.656582	−	0.754254i	$-0.727999\pi$
$491$	7.33922	−	20.1643i	0.331214	−	0.910004i	0.987797	−	0.155749i	$-0.0497792\pi$
$492$	42.0030	−	30.8032i	1.89364	−	1.38871i
$493$		−	4.68930i		−	0.211196i
$494$	27.9415	−	4.05721i	1.25715	−	0.182543i
$495$	−7.07539			−0.318015
$496$	17.4928	−	11.1482i	0.785449	−	0.500568i
$497$	−52.8968	−	19.2529i	−2.37275	−	0.863609i
$498$	42.3612	−	27.6438i	1.89825	−	1.23875i
$499$	−6.43777	+	1.13515i	−0.288194	+	0.0508164i	−0.315876	−	0.948800i	$-0.602298\pi$
$499$	−6.43777	+	1.13515i	−0.288194	+	0.0508164i	0.0276823	+	0.999617i	$0.491187\pi$
$500$	19.3719	−	5.64811i	0.866336	−	0.252591i
$501$	−57.8016	−	33.3717i	−2.58238	−	1.49094i
$502$	−31.8238	−	9.65221i	−1.42037	−	0.430799i
$503$	−17.2486	−	14.4733i	−0.769076	−	0.645331i	0.171396	−	0.985202i	$-0.445172\pi$
$503$	−17.2486	−	14.4733i	−0.769076	−	0.645331i	−0.940472	+	0.339871i	$0.889617\pi$
$504$	65.2534	+	0.703761i	2.90662	+	0.0313480i
$505$	1.04132	+	1.80362i	0.0463381	+	0.0802599i
$506$	−0.144208	−	0.618360i	−0.00641084	−	0.0274895i
$507$	7.54737	+	20.7362i	0.335190	+	0.920928i
$508$	−22.8386	+	2.50314i	−1.01330	+	0.111059i
$509$	25.1079	+	4.42720i	1.11289	+	0.196232i	0.699716	−	0.714421i	$-0.253310\pi$
$509$	25.1079	+	4.42720i	1.11289	+	0.196232i	0.413172	+	0.910653i	$0.364421\pi$
$510$	5.98769	+	14.0194i	0.265139	+	0.620788i
$511$	5.63766	−	4.73056i	0.249395	−	0.209268i
$512$	10.6739	+	19.9516i	0.471724	+	0.881746i
$513$	−8.44590	−	18.0019i	−0.372895	−	0.794802i
$514$	3.11593	+	3.32657i	0.137438	+	0.146729i
$515$	11.2119	+	13.3618i	0.494054	+	0.588791i
$516$	−15.0094	+	34.1192i	−0.660754	+	1.50201i
$517$	1.15460	+	0.203587i	0.0507791	+	0.00895373i
$518$	17.6350	+	13.2276i	0.774839	+	0.581187i
$519$	9.45669	−	3.44195i	0.415102	−	0.151085i
$520$	2.46761	+	14.9346i	0.108212	+	0.654927i
$521$	5.06712	+	8.77650i	0.221994	+	0.384506i	0.955413	−	0.295271i	$-0.0954100\pi$
$521$	5.06712	+	8.77650i	0.221994	+	0.384506i	−0.733419	+	0.679777i	$0.762077\pi$
$522$	−9.22992	+	0.504296i	−0.403983	+	0.0220724i
$523$	14.9088	−	17.7676i	0.651916	−	0.776923i	−0.334286	−	0.942472i	$-0.608495\pi$
$523$	14.9088	−	17.7676i	0.651916	−	0.776923i	0.986202	+	0.165549i	$0.0529396\pi$
$524$	14.5273	+	29.4524i	0.634629	+	1.28663i
$525$	−43.2019	−	24.9426i	−1.88549	−	1.08859i
$526$	23.8257	+	12.0732i	1.03885	+	0.526415i
$527$	−3.00373	−	17.0350i	−0.130845	−	0.742056i
$528$	−4.33044	+	13.7423i	−0.188458	+	0.598057i
$529$	21.5013	+	7.82582i	0.934837	+	0.340253i
$530$	2.10830	+	0.254111i	0.0915787	+	0.0110379i
$531$			43.8940i			1.90484i
$532$	−28.6026	−	32.4557i	−1.24008	−	1.40713i
$533$		−	43.1297i		−	1.86816i
$534$	1.21699	−	10.0971i	0.0526643	−	0.436944i
$535$	7.95290	+	2.89462i	0.343834	+	0.125145i
$536$	−7.50585	+	4.22624i	−0.324203	+	0.182546i
$537$	−0.965698	−	5.47675i	−0.0416729	−	0.236339i
$538$	−13.9810	+	27.5906i	−0.602762	+	1.18952i
$539$	19.8791	+	11.4772i	0.856255	+	0.494359i
$540$	9.56080	−	4.71584i	0.411431	−	0.202938i
$541$	−10.4897	+	12.5011i	−0.450986	+	0.537464i	−0.942854	−	0.333206i	$-0.891870\pi$
$541$	−10.4897	+	12.5011i	−0.450986	+	0.537464i	0.491868	+	0.870670i	$0.336314\pi$
$542$	−0.335070	−	6.13265i	−0.0143925	−	0.263420i
$543$	2.89884	+	5.02093i	0.124401	+	0.215469i
$544$	18.7778	−	1.85336i	0.805093	−	0.0794623i
$545$	0.912511	−	0.332127i	0.0390877	−	0.0142267i
$546$	53.3437	−	71.1178i	2.28290	−	3.04356i
$547$	34.8389	+	6.14305i	1.48961	+	0.262658i	0.858409	−	0.512965i	$-0.171453\pi$
$547$	34.8389	+	6.14305i	1.48961	+	0.262658i	0.631196	+	0.775623i	$0.282564\pi$
$548$	3.45814	−	7.86098i	0.147724	−	0.335805i
$549$	8.83411	+	10.5281i	0.377031	+	0.449328i
$550$	4.88603	−	4.57664i	0.208341	−	0.195149i
$551$	4.34321	+	4.32288i	0.185027	+	0.184161i
$552$	1.71106	+	2.08441i	0.0728277	+	0.0887184i
$553$	−35.4068	+	29.7098i	−1.50565	+	1.26339i
$554$	33.9545	−	14.5020i	1.44259	−	0.616130i
$555$	9.99714	+	1.76276i	0.424355	+	0.0748252i
$556$	1.43376	+	13.0816i	0.0608051	+	0.554784i
$557$	5.98124	+	16.4333i	0.253433	+	0.696302i	0.999536	+	0.0304709i	$0.00970070\pi$
$557$	5.98124	+	16.4333i	0.253433	+	0.696302i	−0.746102	+	0.665831i	$0.768077\pi$
$558$	−33.2068	+	7.74419i	−1.40576	+	0.327838i
$559$	15.4322	+	26.7294i	0.652714	+	1.13053i
$560$	17.0970	−	15.6717i	0.722481	−	0.662251i
$561$	9.20422	+	7.72326i	0.388603	+	0.326076i
$562$	1.30625	−	4.30675i	0.0551006	−	0.181669i
$563$	−20.4832	−	11.8260i	−0.863263	−	0.498405i	0.00184065	−	0.999998i	$-0.499414\pi$
$563$	−20.4832	−	11.8260i	−0.863263	−	0.498405i	−0.865104	+	0.501593i	$0.832747\pi$
$564$	−4.78038	+	1.39378i	−0.201290	+	0.0586888i
$565$	−15.4261	+	2.72003i	−0.648980	+	0.114433i
$566$	−8.21910	−	12.5949i	−0.345475	−	0.529404i
$567$	6.20764	+	2.25940i	0.260696	+	0.0948857i
$568$	−5.91195	+	31.5357i	−0.248060	+	1.32321i
$569$	−24.8034			−1.03981			−0.519907	−	0.854223i	$-0.674033\pi$
$569$	−24.8034			−1.03981			−0.519907	+	0.854223i	$0.674033\pi$
$570$	−18.5045	−	7.37812i	−0.775068	−	0.309035i
$571$			19.2471i			0.805467i	0.915317	+	0.402734i	$0.131940\pi$
$571$			19.2471i			0.805467i	−0.915317	+	0.402734i	$0.868060\pi$
$572$	7.05547	+	9.62079i	0.295004	+	0.402265i
$573$	−3.32544	+	9.13657i	−0.138922	+	0.381686i
$574$	−55.3416	+	36.1144i	−2.30991	+	1.50739i
$575$	−0.217583	−	1.23398i	−0.00907385	−	0.0514604i
$576$	−5.66736	−	36.7610i	−0.236140	−	1.53171i
$577$	−1.47041	+	2.54682i	−0.0612140	+	0.106026i	−0.895008	−	0.446049i	$-0.852831\pi$
$577$	−1.47041	+	2.54682i	−0.0612140	+	0.106026i	0.833794	+	0.552075i	$0.186164\pi$
$578$	−2.41096	+	7.94907i	−0.100283	+	0.330638i
$579$	14.2004	−	16.9234i	0.590149	−	0.703312i
$580$	−2.27162	+	2.37335i	−0.0943237	+	0.0985481i
$581$	−55.5768	+	32.0873i	−2.30571	+	1.33120i
$582$	3.27340	+	14.0362i	0.135687	+	0.581820i
$583$	1.57279	−	0.572447i	0.0651381	−	0.0237083i
$584$	−3.18408	−	2.73082i	−0.131758	−	0.113002i
$585$	4.32082	−	24.5046i	0.178644	−	1.01314i
$586$	−32.9028	+	14.0528i	−1.35920	+	0.580516i
$587$	16.7864	+	20.0052i	0.692847	+	0.825703i	0.991697	−	0.128597i	$-0.0410473\pi$
$587$	16.7864	+	20.0052i	0.692847	+	0.825703i	−0.298850	+	0.954300i	$0.596603\pi$
$588$	−97.2834	−	6.36824i	−4.01190	−	0.262622i
$589$	18.5468	+	12.9218i	0.764206	+	0.532435i
$590$	10.6647	+	11.3856i	0.439058	+	0.468739i
$591$	33.5846	−	28.1808i	1.38148	−	1.15920i
$592$	5.80001	−	11.1462i	0.238379	−	0.458106i
$593$	5.00003	−	28.3566i	0.205326	−	1.16446i	−0.691599	−	0.722282i	$-0.743093\pi$
$593$	5.00003	−	28.3566i	0.205326	−	1.16446i	0.896925	−	0.442182i	$-0.145796\pi$
$594$	5.04173	−	6.72163i	0.206865	−	0.275792i
$595$	−6.61489	−	18.1743i	−0.271184	−	0.745072i
$596$	−12.8049	+	19.1673i	−0.524509	+	0.785124i
$597$	40.6061	−	23.4439i	1.66190	−	0.959496i
$598$	2.22967	−	0.121822i	0.0911778	−	0.00498169i
$599$	2.35865	+	1.97914i	0.0963718	+	0.0808655i	0.689701	−	0.724095i	$-0.257742\pi$
$599$	2.35865	+	1.97914i	0.0963718	+	0.0808655i	−0.593329	+	0.804960i	$0.702187\pi$
$600$	−10.0124	+	26.6124i	−0.408756	+	1.08645i
$601$	16.9867	−	29.4219i	0.692903	−	1.20014i	−0.277979	−	0.960587i	$-0.589665\pi$
$601$	16.9867	−	29.4219i	0.692903	−	1.20014i	0.970882	−	0.239557i	$-0.0770021\pi$
$602$	21.3756	−	42.1835i	0.871204	−	1.71927i
$603$	13.9445	−	2.45879i	0.567864	−	0.100130i
$604$	−25.3319	−	6.19647i	−1.03074	−	0.252131i
$605$	3.71809	−	10.2154i	0.151162	−	0.415313i
$606$	−6.92152	−	0.834242i	−0.281168	−	0.0338888i
$607$	−25.0486			−1.01669			−0.508346	−	0.861153i	$-0.669743\pi$
$607$	−25.0486			−1.01669			−0.508346	+	0.861153i	$0.669743\pi$
$608$	−15.5939	+	19.1005i	−0.632418	+	0.774627i
$609$	19.2945			0.781851
$610$	4.84942	+	0.584495i	0.196347	+	0.0236655i
$611$	−1.41018	+	3.87445i	−0.0570499	+	0.156743i
$612$	−30.1290	−	7.36988i	−1.21789	−	0.297910i
$613$	19.6927	−	3.47236i	0.795382	−	0.140247i	0.238831	−	0.971061i	$-0.423236\pi$
$613$	19.6927	−	3.47236i	0.795382	−	0.140247i	0.556550	+	0.830814i	$0.312125\pi$
$614$	2.50988	−	4.95310i	0.101290	−	0.199891i
$615$	−15.2153	+	26.3537i	−0.613540	+	1.06268i
$616$	6.43699	−	17.1091i	0.259354	−	0.689345i
$617$	−17.0601	−	14.3151i	−0.686813	−	0.576305i	0.231175	−	0.972912i	$-0.425743\pi$
$617$	−17.0601	−	14.3151i	−0.686813	−	0.576305i	−0.917988	+	0.396607i	$0.870187\pi$
$618$	−58.3020	+	3.18545i	−2.34525	+	0.128138i
$619$	11.0491	−	6.37919i	0.444100	−	0.256401i	−0.261235	−	0.965275i	$-0.584130\pi$
$619$	11.0491	−	6.37919i	0.444100	−	0.256401i	0.705335	+	0.708874i	$0.250796\pi$
$620$	−6.73193	+	10.0768i	−0.270361	+	0.404696i
$621$	−0.537869	−	1.47778i	−0.0215839	−	0.0593014i
$622$	3.94191	−	5.25536i	0.158056	−	0.210721i
$623$	−2.24055	+	12.7068i	−0.0897659	+	0.509088i
$624$	−44.9499	−	23.3900i	−1.79944	−	0.936350i
$625$	4.89114	−	4.10415i	0.195645	−	0.164166i
$626$	−18.9918	−	20.2757i	−0.759066	−	0.810380i
$627$	−15.6382	+	1.40516i	−0.624531	+	0.0561165i
$628$	10.4539	+	0.684318i	0.417155	+	0.0273073i
$629$	−6.73510	−	8.02658i	−0.268546	−	0.320041i
$630$	−35.0609	+	14.9745i	−1.39686	+	0.596599i
$631$	−2.33963	+	13.2687i	−0.0931394	+	0.528220i	0.902162	+	0.431397i	$0.141979\pi$
$631$	−2.33963	+	13.2687i	−0.0931394	+	0.528220i	−0.995302	+	0.0968228i	$0.969132\pi$
$632$	19.9973	+	17.1506i	0.795451	+	0.682215i
$633$	15.9196	−	5.79425i	0.632746	−	0.230301i
$634$	−7.69104	−	32.9789i	−0.305450	−	1.30976i
$635$	11.6244	−	6.71136i	0.461301	−	0.266332i
$636$	−4.91526	+	5.13540i	−0.194903	+	0.203632i
$637$	−51.8895	+	61.8395i	−2.05594	+	2.45017i
$638$	−0.751547	+	2.47789i	−0.0297540	+	0.0981005i
$639$	26.3709	−	45.6758i	1.04322	−	1.80691i
$640$	−10.4017	−	8.15843i	−0.411162	−	0.322490i
$641$	2.62021	+	14.8599i	0.103492	+	0.586932i	0.991812	+	0.127707i	$0.0407618\pi$
$641$	2.62021	+	14.8599i	0.103492	+	0.586932i	−0.888320	+	0.459225i	$0.848127\pi$
$642$	−23.7259	+	15.4829i	−0.936386	+	0.611060i
$643$	−13.0609	+	35.8846i	−0.515072	+	1.41515i	0.360817	+	0.932637i	$0.382498\pi$
$643$	−13.0609	+	35.8846i	−0.515072	+	1.41515i	−0.875889	+	0.482512i	$0.839724\pi$
$644$	−2.02331	−	2.75897i	−0.0797297	−	0.108719i
$645$		−	21.7768i		−	0.857459i
$646$	9.73618	+	18.1110i	0.383065	+	0.712566i
$647$	13.0265			0.512126			0.256063	−	0.966660i	$-0.417575\pi$
$647$	13.0265			0.512126			0.256063	+	0.966660i	$0.417575\pi$
$648$	0.693789	−	3.70083i	0.0272546	−	0.145382i
$649$	11.5541	+	4.20536i	0.453539	+	0.165075i
$650$	12.8667	+	19.7169i	0.504674	+	0.773361i
$651$	70.0917	−	12.3591i	2.74711	−	0.484390i
$652$	−12.5438	+	3.65732i	−0.491255	+	0.143232i
$653$	5.04628	+	2.91347i	0.197476	+	0.114013i	0.595478	−	0.803372i	$-0.296963\pi$
$653$	5.04628	+	2.91347i	0.197476	+	0.114013i	−0.398001	+	0.917385i	$0.630296\pi$
$654$	−0.943490	+	3.11073i	−0.0368934	+	0.121639i
$655$	−14.6974	−	12.3326i	−0.574274	−	0.481873i
$656$	25.4513	+	27.7660i	0.993704	+	1.08408i
$657$	3.44768	+	5.97155i	0.134507	+	0.232972i
$658$	6.15228	−	1.43478i	0.239841	−	0.0559335i
$659$	9.27068	+	25.4710i	0.361135	+	0.992209i	0.978629	+	0.205634i	$0.0659256\pi$
$659$	9.27068	+	25.4710i	0.361135	+	0.992209i	−0.617494	+	0.786575i	$0.711852\pi$
$660$	−0.917105	−	8.36765i	−0.0356983	−	0.325710i
$661$	−29.2719	−	5.16143i	−1.13855	−	0.200756i	−0.427576	−	0.903979i	$-0.640633\pi$
$661$	−29.2719	−	5.16143i	−1.13855	−	0.200756i	−0.710969	+	0.703223i	$0.751744\pi$
$662$	10.7267	−	4.58139i	0.416906	−	0.178061i
$663$	−32.3692	+	27.1610i	−1.25712	+	1.05485i
$664$	23.2084	+	28.2724i	0.900662	+	1.09718i
$665$	22.9309	+	10.6274i	0.889223	+	0.412114i
$666$	−15.0744	+	14.1198i	−0.584120	+	0.547133i
$667$	0.311518	+	0.371253i	0.0120620	+	0.0143750i
$668$	19.4346	−	44.1784i	0.751947	−	1.70931i
$669$	7.52794	+	1.32738i	0.291047	+	0.0513194i
$670$	3.01965	−	4.02580i	0.116659	−	0.155530i
$671$	3.61765	−	1.31672i	0.139658	−	0.0508314i
$672$	7.62579	+	77.2627i	0.294171	+	2.98047i
$673$	11.0413	+	19.1240i	0.425609	+	0.737177i	0.996477	−	0.0838649i	$-0.0267264\pi$
$673$	11.0413	+	19.1240i	0.425609	+	0.737177i	−0.570868	+	0.821042i	$0.693393\pi$
$674$	−0.681065	−	12.4653i	−0.0262336	−	0.480144i
$675$	10.6581	−	12.7019i	0.410232	−	0.488896i
$676$	−14.3111	+	7.05892i	−0.550427	+	0.271497i
$677$	41.0192	+	23.6824i	1.57650	+	0.910190i	0.995343	+	0.0963949i	$0.0307312\pi$
$677$	41.0192	+	23.6824i	1.57650	+	0.910190i	0.581152	+	0.813795i	$0.302602\pi$
$678$	23.7012	−	46.7730i	0.910239	−	1.79631i
$679$	−3.17525	−	18.0077i	−0.121855	−	0.691074i
$680$	−9.60574	+	5.40860i	−0.368363	+	0.207410i
$681$	−59.2773	−	21.5752i	−2.27151	−	0.826763i
$682$	−1.14296	+	9.48291i	−0.0437663	+	0.363120i
$683$		−	20.8855i		−	0.799162i	−0.916698	−	0.399581i	$-0.869156\pi$
$683$		−	20.8855i		−	0.799162i	0.916698	−	0.399581i	$-0.130844\pi$
$684$	34.6006	−	21.1113i	1.32299	−	0.807212i
$685$			5.01731i			0.191702i
$686$	74.0267	+	8.92235i	2.82635	+	0.340657i
$687$	52.1467	+	18.9799i	1.98952	+	0.724127i
$688$	−25.7082	−	8.10111i	−0.980117	−	0.308852i
$689$	1.02211	+	5.79669i	0.0389394	+	0.220836i
$690$	−1.40538	−	0.712144i	−0.0535018	−	0.0271109i
$691$	−25.6149	−	14.7888i	−0.974437	−	0.562591i	−0.0738508	−	0.997269i	$-0.523529\pi$
$691$	−25.6149	−	14.7888i	−0.974437	−	0.562591i	−0.900586	+	0.434678i	$0.856862\pi$
$692$	3.21920	+	6.52653i	0.122376	+	0.248102i
$693$	−19.3150	+	23.0187i	−0.733716	+	0.874409i
$694$	−37.4065	+	2.04378i	−1.41993	+	0.0775808i
$695$	−3.84418	−	6.65832i	−0.145818	−	0.252564i
$696$	−1.79278	−	10.8503i	−0.0679550	−	0.411281i
$697$	29.5154	−	10.7427i	1.11798	−	0.406910i
$698$	3.28159	+	2.46144i	0.124210	+	0.0931668i
$699$	−66.2294	−	11.6780i	−2.50503	−	0.441704i
$700$	14.5258	−	33.0197i	0.549022	−	1.24803i
$701$	−21.7671	−	25.9411i	−0.822134	−	0.979781i	0.177857	−	0.984056i	$-0.443083\pi$
$701$	−21.7671	−	25.9411i	−0.822134	−	0.979781i	−0.999991	+	0.00427565i	$0.998639\pi$
$702$	20.2005	+	21.5661i	0.762418	+	0.813959i
$703$	13.6430	+	1.16135i	0.514556	+	0.0438013i
$704$	−10.2195	−	2.03015i	−0.385161	−	0.0765143i
$705$	2.22850	−	1.86993i	0.0839301	−	0.0704257i
$706$	18.3121	+	42.8754i	0.689185	+	1.61364i
$707$	8.71048	+	1.53589i	0.327591	+	0.0577632i
$708$	−51.9109	+	5.68950i	−1.95093	+	0.213824i
$709$	−2.54599	−	6.99505i	−0.0956167	−	0.262705i	0.882659	−	0.470015i	$-0.155751\pi$
$709$	−2.54599	−	6.99505i	−0.0956167	−	0.262705i	−0.978275	+	0.207310i	$0.933529\pi$
$710$	−4.25726	−	18.2550i	−0.159772	−	0.685098i
$711$	−21.6528	−	37.5037i	−0.812043	−	1.40650i
$712$	7.35392	+	0.0793123i	0.275600	+	0.00297235i
$713$	1.36947	+	1.14912i	0.0512870	+	0.0430349i
$714$	61.9556	+	18.7913i	2.31863	+	0.703245i
$715$	−6.03632	−	3.48507i	−0.225746	−	0.130334i
$716$	3.86074	−	1.12565i	0.144283	−	0.0420675i
$717$	3.51812	−	0.620339i	0.131386	−	0.0231670i
$718$	6.51233	−	4.24977i	0.243038	−	0.158600i
$719$	−3.11284	−	1.13298i	−0.116090	−	0.0422531i	0.283322	−	0.959025i	$-0.408563\pi$
$719$	−3.11284	−	1.13298i	−0.116090	−	0.0422531i	−0.399412	+	0.916772i	$0.630786\pi$
$720$	11.6787	+	18.3253i	0.435241	+	0.682942i
$721$	74.0778			2.75880
$722$	−25.7497	−	7.67814i	−0.958304	−	0.285751i
$723$			34.6472i			1.28854i
$724$	−3.38079	+	2.47932i	−0.125646	+	0.0921434i
$725$	−1.74766	+	4.80165i	−0.0649064	+	0.178329i
$726$	19.8875	+	30.4755i	0.738093	+	1.13105i
$727$	−6.44524	−	36.5528i	−0.239041	−	1.35567i	−0.833935	−	0.551863i	$-0.813917\pi$
$727$	−6.44524	−	36.5528i	−0.239041	−	1.35567i	0.594894	−	0.803804i	$-0.297194\pi$
$728$	55.3239	+	32.7418i	2.05044	+	1.21349i
$729$	−22.0202	+	38.1401i	−0.815563	+	1.41260i
$730$	2.34516	+	0.711292i	0.0867984	+	0.0263261i
$731$	−14.4482	+	17.2187i	−0.534385	+	0.636856i
$732$	−11.3059	+	11.8122i	−0.417878	+	0.436593i
$733$	−16.8038	+	9.70169i	−0.620663	+	0.358340i	−0.777127	−	0.629344i	$-0.783324\pi$
$733$	−16.8038	+	9.70169i	−0.620663	+	0.358340i	0.156464	+	0.987684i	$0.449990\pi$
$734$	−21.1188	+	4.92513i	−0.779508	+	0.181790i
$735$	53.5220	−	19.4804i	1.97419	−	0.718546i
$736$	−1.36352	+	1.39417i	−0.0502601	+	0.0513899i
$737$	0.688759	−	3.90615i	0.0253708	−	0.143885i
$738$	−24.3190	−	56.9397i	−0.895194	−	2.09598i
$739$	−10.2329	−	12.1951i	−0.376424	−	0.448604i	0.544258	−	0.838918i	$-0.316811\pi$
$739$	−10.2329	−	12.1951i	−0.376424	−	0.448604i	−0.920682	+	0.390313i	$0.872367\pi$
$740$	−0.479504	+	7.32507i	−0.0176269	+	0.269275i
$741$	4.68345	−	55.0189i	0.172051	−	2.02117i
$742$	6.58213	−	6.16534i	0.241638	−	0.226337i
$743$	27.2271	−	22.8462i	0.998864	−	0.838146i	0.0120371	−	0.999928i	$-0.496168\pi$
$743$	27.2271	−	22.8462i	0.998864	−	0.838146i	0.986827	+	0.161781i	$0.0517239\pi$
$744$	−13.4629	−	38.2680i	−0.493572	−	1.40297i
$745$	2.33852	−	13.2624i	0.0856766	−	0.485896i
$746$	5.78042	+	4.33575i	0.211636	+	0.158743i
$747$	−20.5649	−	56.5015i	−0.752429	−	2.06728i
$748$	−4.82652	+	7.22469i	−0.176475	+	0.264161i
$749$	31.1277	−	17.9716i	1.13738	−	0.656668i
$750$	−2.15291	−	39.4039i	−0.0786133	−	1.43883i
$751$	−2.42869	−	2.03791i	−0.0886241	−	0.0743644i	0.597399	−	0.801944i	$-0.296201\pi$
$751$	−2.42869	−	2.03791i	−0.0886241	−	0.0743644i	−0.686023	+	0.727580i	$0.740645\pi$
$752$	−1.37850	−	3.32645i	−0.0502688	−	0.121303i
$753$	−32.5185	+	56.3237i	−1.18504	+	2.05255i
$754$	−8.12284	−	4.11608i	−0.295816	−	0.149899i
$755$	15.0044	−	2.64567i	0.546065	−	0.0962859i
$756$	10.7576	−	43.9783i	0.391250	−	1.59948i
$757$	11.4478	−	31.4527i	0.416079	−	1.14317i	−0.537825	−	0.843056i	$-0.680754\pi$
$757$	11.4478	−	31.4527i	0.416079	−	1.14317i	0.953904	−	0.300111i	$-0.0970239\pi$
$758$	−6.24256	+	51.7931i	−0.226740	+	1.88121i
$759$	−1.24177			−0.0450733
$760$	3.84572	−	13.8828i	0.139499	−	0.503581i
$761$	5.70478			0.206798			0.103399	−	0.994640i	$-0.467028\pi$
$761$	5.70478			0.206798			0.103399	+	0.994640i	$0.467028\pi$
$762$	−5.37674	+	44.6096i	−0.194779	+	1.61604i
$763$	1.41053	−	3.87539i	0.0510644	−	0.140298i
$764$	−6.82959	−	1.67059i	−0.247086	−	0.0604399i
$765$	17.8457	−	3.14668i	0.645213	−	0.113768i
$766$	−39.8883	−	20.2125i	−1.44122	−	0.730308i
$767$	−21.6205	+	37.4479i	−0.780672	+	1.35216i
$768$	42.7405	−	11.4674i	1.54226	−	0.413794i
$769$	−21.0908	−	17.6973i	−0.760553	−	0.638179i	0.177718	−	0.984081i	$-0.443128\pi$
$769$	−21.0908	−	17.6973i	−0.760553	−	0.638179i	−0.938271	+	0.345902i	$0.887573\pi$
$770$	0.582631	+	10.6637i	0.0209966	+	0.384292i
$771$	7.71970	−	4.45697i	0.278018	−	0.160514i
$772$	13.2837	+	8.87431i	0.478092	+	0.319394i
$773$	7.83088	+	21.5152i	0.281657	+	0.773847i	0.997165	+	0.0752423i	$0.0239730\pi$
$773$	7.83088	+	21.5152i	0.281657	+	0.773847i	−0.715508	+	0.698604i	$0.753805\pi$
$774$	35.4452	+	26.5865i	1.27405	+	0.955633i
$775$	−3.27309	+	18.5626i	−0.117573	+	0.666788i
$776$	−9.83170	+	3.45883i	−0.352938	+	0.124165i
$777$	33.0259	−	27.7120i	1.18480	−	0.994164i
$778$	−5.87756	+	5.50539i	−0.210721	+	0.197378i
$779$	−17.2592	+	37.2404i	−0.618375	+	1.33427i
$780$	29.5402	+	1.93372i	1.05771	+	0.0692383i
$781$	−9.49662	−	11.3176i	−0.339816	−	0.404976i
$782$	0.638733	+	1.49551i	0.0228410	+	0.0534793i
$783$	−1.11364	+	6.31577i	−0.0397982	+	0.225707i
$784$	−3.08674	−	70.4315i	−0.110241	−	2.51541i
$785$	−5.75137	+	2.09333i	−0.205275	+	0.0747140i
$786$	62.5469	−	14.5866i	2.23097	−	0.520287i
$787$	−19.6299	+	11.3333i	−0.699730	+	0.403989i	−0.807247	−	0.590214i	$-0.799043\pi$
$787$	−19.6299	+	11.3333i	−0.699730	+	0.403989i	0.107517	+	0.994203i	$0.465710\pi$
$788$	22.9030	+	21.9212i	0.815885	+	0.780911i
$789$	33.5769	−	40.0154i	1.19537	−	1.42459i
$790$	−14.7286	−	4.46720i	−0.524019	−	0.158936i
$791$	−33.2622	+	57.6118i	−1.18267	+	2.04844i
$792$	14.7394	+	8.72306i	0.523741	+	0.309960i
$793$	2.35102	+	13.3333i	0.0834873	+	0.473480i
$794$	−6.59850	−	10.1115i	−0.234172	−	0.358844i
$795$	1.42041	−	3.90255i	0.0503769	−	0.138409i
$796$	20.0512	+	27.3416i	0.710696	+	0.969099i
$797$		−	53.3671i		−	1.89036i	−0.326550	−	0.945180i	$-0.605886\pi$
$797$		−	53.3671i		−	1.89036i	0.326550	−	0.945180i	$-0.394114\pi$
$798$	−74.5188	+	40.0602i	−2.63794	+	1.41812i
$799$	−3.00269			−0.106228
$800$	−19.9185	−	5.10055i	−0.704224	−	0.180332i
$801$	−11.3601	−	4.13474i	−0.401390	−	0.146094i
$802$	−17.0446	+	11.1228i	−0.601864	+	0.392760i
$803$	1.90219	−	0.335407i	0.0671268	−	0.0118363i
$804$	4.71534	+	16.1726i	0.166297	+	0.570365i
$805$	1.73105	+	0.999421i	0.0610114	+	0.0352249i
$806$	−32.1447	−	9.74954i	−1.13225	−	0.343413i
$807$	46.3386	+	38.8827i	1.63120	+	1.36874i
$808$	0.0543683	−	5.04109i	0.00191267	−	0.177345i
$809$	15.6437	+	27.0958i	0.550005	+	0.952636i	0.998273	+	0.0587375i	$0.0187075\pi$
$809$	15.6437	+	27.0958i	0.550005	+	0.952636i	−0.448269	+	0.893899i	$0.647959\pi$
$810$	0.499605	+	2.14229i	0.0175543	+	0.0752724i
$811$	3.73492	+	10.2616i	0.131151	+	0.360334i	0.987835	−	0.155508i	$-0.0497014\pi$
$811$	3.73492	+	10.2616i	0.131151	+	0.360334i	−0.856684	+	0.515842i	$0.827479\pi$
$812$	1.52010	+	13.8693i	0.0533450	+	0.486719i
$813$	−11.8289	−	2.08576i	−0.414859	−	0.0731508i
$814$	2.27251	+	5.32077i	0.0796513	+	0.186493i
$815$	5.84763	−	4.90675i	0.204834	−	0.171876i
$816$	4.81064	−	36.5871i	0.168406	−	1.28080i
$817$	−2.62868	−	29.2550i	−0.0919658	−	1.02350i
$818$	−15.2481	−	16.2788i	−0.533136	−	0.569176i
$819$	−67.9266	−	80.9518i	−2.37355	−	2.82868i
$820$	−20.1424	−	8.86089i	−0.703404	−	0.309436i
$821$	42.3926	+	7.47495i	1.47951	+	0.260878i	0.854383	−	0.519645i	$-0.173936\pi$
$821$	42.3926	+	7.47495i	1.47951	+	0.260878i	0.625128	+	0.780522i	$0.285047\pi$
$822$	−13.4359	−	10.0779i	−0.468629	−	0.351507i
$823$	−49.8514	+	18.1444i	−1.73771	+	0.632475i	−0.999131	−	0.0416894i	$-0.986726\pi$
$823$	−49.8514	+	18.1444i	−1.73771	+	0.632475i	−0.738581	+	0.674165i	$0.764504\pi$
$824$	−6.88305	−	41.6580i	−0.239782	−	1.45122i
$825$	−6.54636	−	11.3386i	−0.227915	−	0.394760i
$826$	66.1548	−	3.61450i	2.30182	−	0.125765i
$827$	11.9473	−	14.2382i	0.415447	−	0.495111i	−0.517218	−	0.855854i	$-0.673032\pi$
$827$	11.9473	−	14.2382i	0.415447	−	0.495111i	0.932665	+	0.360743i	$0.117477\pi$
$828$	2.87491	−	1.41804i	0.0999099	−	0.0492804i
$829$	21.1582	+	12.2157i	0.734855	+	0.424269i	0.820196	−	0.572083i	$-0.193864\pi$
$829$	21.1582	+	12.2157i	0.734855	+	0.424269i	−0.0853405	+	0.996352i	$0.527198\pi$
$830$	−19.0622	−	9.65934i	−0.661657	−	0.335281i
$831$	−12.5387	−	71.1103i	−0.434961	−	2.46679i
$832$	13.2720	−	34.1539i	0.460124	−	1.18407i
$833$	−55.2440	−	20.1072i	−1.91409	−	0.696672i
$834$	25.5518	+	3.07973i	0.884787	+	0.106642i
$835$			28.1971i			0.975800i
$836$	−2.24211	−	11.1305i	−0.0775449	−	0.384955i
$837$			23.6568i			0.817700i
$838$	4.01540	−	33.3148i	0.138710	−	1.15084i
$839$	17.9030	+	6.51614i	0.618079	+	0.224962i	0.632034	−	0.774940i	$-0.282220\pi$
$839$	17.9030	+	6.51614i	0.618079	+	0.224962i	−0.0139558	+	0.999903i	$0.504442\pi$
$840$	−22.2541	−	39.5235i	−0.767838	−	1.36369i
$841$	4.69261	+	26.6131i	0.161814	+	0.917693i
$842$	20.3290	−	40.1181i	0.700584	−	1.38256i
$843$	−7.62235	−	4.40077i	−0.262528	−	0.151571i
$844$	5.41926	+	10.9869i	0.186539	+	0.378184i
$845$	5.99248	−	7.14156i	0.206148	−	0.245677i
$846$	0.322915	+	5.91018i	0.0111020	+	0.203196i
$847$	−23.0842	−	39.9830i	−0.793182	−	1.37383i
$848$	−4.07870	−	3.12863i	−0.140063	−	0.107437i
$849$	−27.6387	+	10.0597i	−0.948557	+	0.345246i
$850$	−10.2883	+	13.7163i	−0.352884	+	0.470466i
$851$	1.06644	+	0.188042i	0.0365570	+	0.00644599i
$852$	57.4363	+	25.2669i	1.96773	+	0.865630i
$853$	31.1024	+	37.0663i	1.06492	+	1.26913i	0.961593	+	0.274480i	$0.0885058\pi$
$853$	31.1024	+	37.0663i	1.06492	+	1.26913i	0.103332	+	0.994647i	$0.467050\pi$
$854$	15.1399	−	14.1813i	0.518078	−	0.485273i
$855$	−13.5368	+	19.4294i	−0.462948	+	0.664472i
$856$	−12.9987	−	15.8350i	−0.444286	−	0.541228i
$857$	−17.6458	+	14.8066i	−0.602769	+	0.505783i	−0.892334	−	0.451375i	$-0.850934\pi$
$857$	−17.6458	+	14.8066i	−0.602769	+	0.505783i	0.289565	+	0.957158i	$0.406489\pi$
$858$	21.4574	−	9.16445i	0.732542	−	0.312869i
$859$	−19.7092	−	3.47526i	−0.672469	−	0.118574i	−0.173021	−	0.984918i	$-0.555353\pi$
$859$	−19.7092	−	3.47526i	−0.672469	−	0.118574i	−0.499448	+	0.866344i	$0.666464\pi$
$860$	15.6537	−	1.71566i	0.533786	−	0.0585036i
$861$	44.2017	+	121.443i	1.50639	+	4.13878i
$862$	11.8017	−	2.75227i	0.401966	−	0.0937428i
$863$	−10.6842	−	18.5056i	−0.363695	−	0.629938i	0.624871	−	0.780728i	$-0.285152\pi$
$863$	−10.6842	−	18.5056i	−0.363695	−	0.629938i	−0.988566	+	0.150790i	$0.951818\pi$
$864$	−25.7310	−	1.96326i	−0.875386	−	0.0667915i
$865$	−3.25688	−	2.73285i	−0.110737	−	0.0929197i
$866$	−2.08115	+	6.86164i	−0.0707202	+	0.233168i
$867$	14.0687	+	8.12259i	0.477800	+	0.275858i
$868$	14.4061	+	49.4100i	0.488975	+	1.67708i
$869$	−11.9465	+	2.10649i	−0.405258	+	0.0714579i
$870$	3.51126	+	5.38064i	0.119043	+	0.182421i
$871$	13.1078	+	4.77083i	0.444139	+	0.161654i
$872$	−2.31040	−	0.433128i	−0.0782401	−	0.0146676i
$873$	17.1324			0.579845
$874$	−1.97396	−	0.787056i	−0.0667700	−	0.0266226i
$875$			50.0661i			1.69254i
$876$	−6.61532	+	4.85139i	−0.223511	+	0.163913i
$877$	−13.0625	+	35.8890i	−0.441090	+	1.21188i	0.497687	+	0.867357i	$0.334183\pi$
$877$	−13.0625	+	35.8890i	−0.441090	+	1.21188i	−0.938776	+	0.344527i	$0.888039\pi$
$878$	31.7134	−	20.6953i	1.07028	−	0.698432i
$879$	12.1503	+	68.9077i	0.409819	+	2.32420i
$880$	5.94262	−	1.31848i	0.200326	−	0.0444458i
$881$	4.34259	−	7.52159i	0.146306	−	0.253409i	−0.783554	−	0.621324i	$-0.786595\pi$
$881$	4.34259	−	7.52159i	0.146306	−	0.253409i	0.929859	+	0.367915i	$0.119928\pi$
$882$	−33.6357	+	110.899i	−1.13257	+	3.73415i
$883$	6.54988	−	7.80584i	0.220421	−	0.262687i	−0.644490	−	0.764613i	$-0.722930\pi$
$883$	6.54988	−	7.80584i	0.220421	−	0.262687i	0.864911	+	0.501925i	$0.167375\pi$
$884$	−22.0742	−	21.1280i	−0.742436	−	0.710610i
$885$	26.4217	−	15.2546i	0.888157	−	0.512777i
$886$	−10.1648	−	43.5863i	−0.341493	−	1.46431i
$887$	−14.4753	+	5.26857i	−0.486032	+	0.176901i	−0.573401	−	0.819275i	$-0.694376\pi$
$887$	−14.4753	+	5.26857i	−0.486032	+	0.176901i	0.0873688	+	0.996176i	$0.472154\pi$
$888$	−18.6527	−	15.9974i	−0.625942	−	0.536837i
$889$	9.89892	−	56.1396i	0.331999	−	1.88286i
$890$	−3.95128	+	1.68760i	−0.132447	+	0.0565683i
$891$	1.11446	+	1.32816i	0.0373359	+	0.0444952i
$892$	−0.361071	+	5.51585i	−0.0120895	+	0.184684i
$893$	2.76806	−	2.78108i	0.0926296	−	0.0930654i
$894$	30.8181	+	32.9015i	1.03071	+	1.10039i
$895$	−1.79978	+	1.51020i	−0.0601601	+	0.0504803i
$896$	−54.9376	+	11.5687i	−1.83534	+	0.386483i
$897$	0.758326	−	4.30068i	0.0253198	−	0.143596i
$898$	−5.51117	+	7.34749i	−0.183910	+	0.245189i
$899$	−2.49344	−	6.85068i	−0.0831610	−	0.228483i
$900$	28.1041	+	18.7752i	0.936804	+	0.625841i
$901$	−3.71233	+	2.14331i	−0.123676	+	0.0714041i
$902$	−17.3180	+	0.946207i	−0.576628	+	0.0315052i
$903$	−70.8474	−	59.4480i	−2.35765	−	1.97831i
$904$	35.4889	+	13.3521i	1.18034	+	0.444083i
$905$	1.22467	−	2.12119i	0.0407094	−	0.0705107i
$906$	−23.0533	+	45.4943i	−0.765894	+	1.51145i
$907$	−5.96261	+	1.05137i	−0.197985	+	0.0349101i	−0.271761	−	0.962365i	$-0.587606\pi$
$907$	−5.96261	+	1.05137i	−0.197985	+	0.0349101i	0.0737760	+	0.997275i	$0.476495\pi$
$908$	10.8387	−	44.3098i	0.359694	−	1.47047i
$909$	−2.83435	+	7.78732i	−0.0940095	+	0.258289i
$910$	−37.2878	−	4.49426i	−1.23608	−	0.148983i
$911$	10.2759			0.340454			0.170227	−	0.985405i	$-0.445550\pi$
$911$	10.2759			0.340454			0.170227	+	0.985405i	$0.445550\pi$
$912$	29.4521	+	38.1837i	0.975255	+	1.26439i
$913$	−16.8430			−0.557423
$914$	10.5826	+	1.27551i	0.350042	+	0.0421901i
$915$	3.26718	−	8.97649i	0.108009	−	0.296754i
$916$	−9.53486	+	38.9797i	−0.315041	+	1.28793i
$917$	−80.2444	+	14.1492i	−2.64990	+	0.467249i
$918$	−9.72701	+	19.1957i	−0.321039	+	0.633552i
$919$	−20.0078	+	34.6546i	−0.659998	+	1.14315i	0.320618	+	0.947209i	$0.396109\pi$
$919$	−20.0078	+	34.6546i	−0.659998	+	1.14315i	−0.980616	+	0.195941i	$0.937224\pi$
$920$	0.401186	−	1.06633i	0.0132267	−	0.0351557i
$921$	−8.31876	−	6.98027i	−0.274112	−	0.230008i
$922$	−18.1480	+	0.991553i	−0.597672	+	0.0326550i
$923$	44.9964	−	25.9787i	1.48107	−	0.855098i
$924$	−29.7265	−	19.8591i	−0.977930	−	0.653315i
$925$	3.90504	+	10.7290i	0.128397	+	0.352767i
$926$	9.84490	−	13.1252i	0.323523	−	0.431321i
$927$	−12.0523	+	68.3519i	−0.395849	+	2.24497i
$928$	7.65825	−	2.14353i	0.251394	−	0.0703647i
$929$	37.3140	−	31.3102i	1.22423	−	1.02725i	0.225640	−	0.974211i	$-0.427553\pi$
$929$	37.3140	−	31.3102i	1.22423	−	1.02725i	0.998592	−	0.0530419i	$-0.0168917\pi$
$930$	16.2020	+	17.2973i	0.531285	+	0.567201i
$931$	69.5503	−	32.6308i	2.27942	−	1.06943i
$932$	3.17663	−	48.5274i	0.104054	−	1.58957i
$933$	−8.25837	−	9.84195i	−0.270367	−	0.322211i
$934$	−19.2179	+	8.20800i	−0.628830	+	0.268574i
$935$	0.881452	−	4.99896i	0.0288266	−	0.163484i
$936$	−39.2121	+	45.7206i	−1.28169	+	1.49442i
$937$	5.03883	−	1.83398i	0.164611	−	0.0599136i	−0.258400	−	0.966038i	$-0.583195\pi$
$937$	5.03883	−	1.83398i	0.164611	−	0.0599136i	0.423011	+	0.906124i	$0.360973\pi$
$938$	−4.85404	−	20.8140i	−0.158490	−	0.679600i
$939$	−47.0522	+	27.1656i	−1.53549	+	0.886516i
$940$	1.51972	+	1.45458i	0.0495679	+	0.0474431i
$941$	−14.8151	+	17.6560i	−0.482959	+	0.575568i	−0.951412	−	0.307920i	$-0.900367\pi$
$941$	−14.8151	+	17.6560i	−0.482959	+	0.575568i	0.468453	+	0.883488i	$0.344812\pi$
$942$	5.94662	−	19.6063i	0.193751	−	0.638807i
$943$	−1.62308	+	2.81126i	−0.0528549	+	0.0915473i
$944$	−8.17951	−	36.8666i	−0.266220	−	1.19991i
$945$	4.59311	+	26.0488i	0.149414	+	0.847369i
$946$	10.3942	−	6.78298i	0.337945	−	0.220534i
$947$	−20.4194	+	56.1020i	−0.663543	+	1.82307i	−0.103457	+	0.994634i	$0.532991\pi$
$947$	−20.4194	+	56.1020i	−0.663543	+	1.82307i	−0.560085	+	0.828435i	$0.689232\pi$
$948$	41.5469	−	30.4687i	1.34938	−	0.989578i
$949$			6.79278i			0.220503i
$950$	−3.21967	−	22.1735i	−0.104460	−	0.719402i
$951$	−66.2271			−2.14756
$952$	−8.62650	+	46.0157i	−0.279586	+	1.49138i
$953$	42.5479	+	15.4862i	1.37826	+	0.501646i	0.921651	−	0.388020i	$-0.126841\pi$
$953$	42.5479	+	15.4862i	1.37826	+	0.501646i	0.456611	+	0.889666i	$0.349063\pi$
$954$	4.61790	+	7.07645i	0.149510	+	0.229109i
$955$	4.04524	−	0.713284i	0.130901	−	0.0230813i
$956$	0.723087	+	2.48004i	0.0233863	+	0.0802101i
$957$	4.38552	+	2.53198i	0.141764	+	0.0818473i
$958$	12.9556	−	42.7153i	0.418577	−	1.38007i
$959$	16.3231	+	13.6967i	0.527100	+	0.442289i
$960$	−20.1584	+	16.1871i	−0.650611	+	0.522435i
$961$	2.05378	+	3.55725i	0.0662510	+	0.114750i
$962$	−19.8155	+	4.62119i	−0.638877	+	0.148993i
$963$	11.5181	+	31.6457i	0.371165	+	1.01977i
$964$	−24.9053	+	2.72965i	−0.802145	+	0.0879161i
$965$	−9.19136	−	1.62069i	−0.295880	−	0.0521717i
$966$	−6.15337	+	2.62811i	−0.197981	+	0.0845580i
$967$	−22.7479	+	19.0878i	−0.731523	+	0.613821i	−0.930546	−	0.366174i	$-0.880668\pi$
$967$	−22.7479	+	19.0878i	−0.731523	+	0.613821i	0.199023	+	0.979995i	$0.436223\pi$
$968$	−20.3397	+	16.6966i	−0.653743	+	0.536648i
$969$	38.8182	−	10.4990i	1.24702	−	0.337277i
$970$	4.44397	−	4.16257i	0.142687	−	0.133652i
$971$	9.84719	+	11.7354i	0.316011	+	0.376608i	0.900546	−	0.434761i	$-0.143167\pi$
$971$	9.84719	+	11.7354i	0.316011	+	0.376608i	−0.584534	+	0.811369i	$0.698723\pi$
$972$	−31.7944	−	13.9867i	−1.01981	−	0.448625i
$973$	−32.1560	−	5.66997i	−1.03087	−	0.181771i
$974$	−12.1776	+	16.2352i	−0.390195	+	0.520208i
$975$	43.2674	−	15.7480i	1.38567	−	0.504341i
$976$	−9.38165	−	7.19634i	−0.300299	−	0.230349i
$977$	−10.5550	−	18.2817i	−0.337683	−	0.584884i	0.646314	−	0.763072i	$-0.276310\pi$
$977$	−10.5550	−	18.2817i	−0.337683	−	0.584884i	−0.983996	+	0.178188i	$0.942976\pi$
$978$	1.39407	+	25.5152i	0.0445776	+	0.815886i
$979$	−2.17676	+	2.59416i	−0.0695695	+	0.0829097i
$980$	18.2197	+	36.9382i	0.582007	+	1.17995i
$981$	3.34635	+	1.93202i	0.106841	+	0.0616845i
$982$	13.7170	−	27.0698i	0.437728	−	0.863831i
$983$	7.39972	+	41.9659i	0.236014	+	1.33850i	0.840467	+	0.541863i	$0.182281\pi$
$983$	7.39972	+	41.9659i	0.236014	+	1.33850i	−0.604452	+	0.796641i	$0.706608\pi$
$984$	64.1871	−	36.1411i	2.04621	−	1.15214i
$985$	−17.4047	−	6.33479i	−0.554560	−	0.201843i
$986$	0.793565	−	6.58403i	0.0252722	−	0.209678i
$987$		−	12.3548i		−	0.393257i
$988$	39.9179	−	0.968031i	1.26996	−	0.0307972i
$989$		−	2.32302i		−	0.0738678i
$990$	−9.93421	−	1.19736i	−0.315730	−	0.0380545i
$991$	18.8672	+	6.86709i	0.599336	+	0.218140i	0.623831	−	0.781560i	$-0.285576\pi$
$991$	18.8672	+	6.86709i	0.599336	+	0.218140i	−0.0244949	+	0.999700i	$0.507798\pi$
$992$	26.4474	−	12.6923i	0.839704	−	0.402982i
$993$	−3.96115	−	22.4648i	−0.125703	−	0.712899i
$994$	−71.0118	−	35.9837i	−2.25236	−	1.14133i
$995$	−17.1548	−	9.90434i	−0.543844	−	0.313989i
$996$	64.1555	−	31.6446i	2.03284	−	1.00270i
$997$	−21.3831	+	25.4834i	−0.677211	+	0.807068i	−0.989746	−	0.142838i	$-0.954377\pi$
$997$	−21.3831	+	25.4834i	−0.677211	+	0.807068i	0.312535	+	0.949906i	$0.398822\pi$
$998$	−9.23106	+	0.504358i	−0.292204	+	0.0159652i
$999$	7.16495	+	12.4100i	0.226689	+	0.392637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.t.a.101.18	yes	108
4.3	odd	2		608.2.bf.a.177.3		108
8.3	odd	2		608.2.bf.a.177.16		108
8.5	even	2	inner	152.2.t.a.101.10	✓	108
19.16	even	9	inner	152.2.t.a.149.10	yes	108
76.35	odd	18		608.2.bf.a.529.16		108
152.35	odd	18		608.2.bf.a.529.3		108
152.149	even	18	inner	152.2.t.a.149.18	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.10	✓	108	8.5	even	2	inner
152.2.t.a.101.18	yes	108	1.1	even	1	trivial
152.2.t.a.149.10	yes	108	19.16	even	9	inner
152.2.t.a.149.18	yes	108	152.149	even	18	inner
608.2.bf.a.177.3		108	4.3	odd	2
608.2.bf.a.177.16		108	8.3	odd	2
608.2.bf.a.529.3		108	152.35	odd	18
608.2.bf.a.529.16		108	76.35	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40405 + 0.169229i) q^{2} +(0.945944 - 2.59896i) q^{3} +(1.94272 + 0.475212i) q^{4} +(-1.15070 + 0.202899i) q^{5} +(1.76797 - 3.48899i) q^{6} +(-2.48117 + 4.29751i) q^{7} +(2.64726 + 0.995986i) q^{8} +(-3.56165 - 2.98858i) q^{9} +O(q^{10})\)	\(q+(1.40405 + 0.169229i) q^{2} +(0.945944 - 2.59896i) q^{3} +(1.94272 + 0.475212i) q^{4} +(-1.15070 + 0.202899i) q^{5} +(1.76797 - 3.48899i) q^{6} +(-2.48117 + 4.29751i) q^{7} +(2.64726 + 0.995986i) q^{8} +(-3.56165 - 2.98858i) q^{9} +(-1.64997 + 0.0901496i) q^{10} +(-1.12791 + 0.651199i) q^{11} +(3.07276 - 4.59954i) q^{12} +(-1.56654 - 4.30402i) q^{13} +(-4.21095 + 5.61404i) q^{14} +(-0.561168 + 3.18254i) q^{15} +(3.54835 + 1.84641i) q^{16} +(2.55523 - 2.14409i) q^{17} +(-4.49499 - 4.79886i) q^{18} +(-0.369712 + 4.34319i) q^{19} +(-2.33190 - 0.152648i) q^{20} +(8.82201 + 10.5137i) q^{21} +(-1.69384 + 0.723442i) q^{22} +(-0.0598623 + 0.339496i) q^{23} +(5.09269 - 5.93799i) q^{24} +(-3.41553 + 1.24315i) q^{25} +(-1.47113 - 6.30818i) q^{26} +(-3.95069 + 2.28093i) q^{27} +(-6.86245 + 7.16979i) q^{28} +(0.903650 - 1.07693i) q^{29} +(-1.32649 + 4.37349i) q^{30} +(2.59290 - 4.49103i) q^{31} +(4.66960 + 3.19294i) q^{32} +(0.625501 + 3.54739i) q^{33} +(3.95051 - 2.57800i) q^{34} +(1.98311 - 5.44855i) q^{35} +(-5.49910 - 7.49853i) q^{36} -3.14124i q^{37} +(-1.25409 + 6.03550i) q^{38} -12.6678 q^{39} +(-3.24828 - 0.608951i) q^{40} +(8.84858 + 3.22062i) q^{41} +(10.6073 + 16.2547i) q^{42} +(-6.63623 + 1.17015i) q^{43} +(-2.50067 + 0.729103i) q^{44} +(4.70476 + 2.71629i) q^{45} +(-0.141502 + 0.466539i) q^{46} +(-0.689587 - 0.578632i) q^{47} +(8.15528 - 7.47542i) q^{48} +(-8.81238 - 15.2635i) q^{49} +(-5.00596 + 1.16744i) q^{50} +(-3.15530 - 8.66913i) q^{51} +(-0.998025 - 9.10596i) q^{52} +(-1.26559 - 0.223157i) q^{53} +(-5.93297 + 2.53397i) q^{54} +(1.16575 - 0.978183i) q^{55} +(-10.8486 + 8.90543i) q^{56} +(10.9381 + 5.06928i) q^{57} +(1.45102 - 1.35914i) q^{58} +(-6.06841 - 7.23205i) q^{59} +(-2.60258 + 5.91613i) q^{60} +(-2.91105 - 0.513296i) q^{61} +(4.40057 - 5.86684i) q^{62} +(21.6805 - 7.89106i) q^{63} +(6.01602 + 5.27328i) q^{64} +(2.67589 + 4.63477i) q^{65} +(0.277915 + 5.08657i) q^{66} +(-1.95759 + 2.33296i) q^{67} +(5.98300 - 2.95110i) q^{68} +(0.825710 + 0.476724i) q^{69} +(3.70644 - 7.31445i) q^{70} +(1.96983 + 11.1714i) q^{71} +(-6.45205 - 11.4589i) q^{72} +(-1.39362 - 0.507236i) q^{73} +(0.531588 - 4.41046i) q^{74} +10.0528i q^{75} +(-2.78218 + 8.26193i) q^{76} -6.46293i q^{77} +(-17.7863 - 2.14376i) q^{78} +(8.75250 + 3.18565i) q^{79} +(-4.45770 - 1.40470i) q^{80} +(-0.231166 - 1.31101i) q^{81} +(11.8788 + 6.01935i) q^{82} +(11.1997 + 6.46616i) q^{83} +(12.1425 + 24.6175i) q^{84} +(-2.50526 + 2.98565i) q^{85} +(-9.51564 + 0.519906i) q^{86} +(-1.94409 - 3.36726i) q^{87} +(-3.63446 + 0.600514i) q^{88} +(2.44335 - 0.889305i) q^{89} +(6.14605 + 4.61000i) q^{90} +(22.3834 + 3.94680i) q^{91} +(-0.277628 + 0.631099i) q^{92} +(-9.21927 - 10.9871i) q^{93} +(-0.870295 - 0.929128i) q^{94} +(-0.455802 - 5.07271i) q^{95} +(12.7155 - 9.11576i) q^{96} +(-2.82277 + 2.36859i) q^{97} +(-9.79002 - 22.9220i) q^{98} +(5.96338 + 1.05151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

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